diff --git a/qiskit/assembler/assemble_circuits.py b/qiskit/assembler/assemble_circuits.py
index b91a269fa23a..6b85ccc29043 100644
--- a/qiskit/assembler/assemble_circuits.py
+++ b/qiskit/assembler/assemble_circuits.py
@@ -76,7 +76,7 @@ def _assemble_circuit(
                                   memory_slots=memory_slots,
                                   creg_sizes=creg_sizes,
                                   name=circuit.name,
-                                  global_phase=circuit.global_phase)
+                                  global_phase=float(circuit.global_phase))
 
     # TODO: why do we need n_qubits and memory_slots in both the header and the config
     config = QasmQobjExperimentConfig(n_qubits=num_qubits, memory_slots=memory_slots)
@@ -113,6 +113,9 @@ def _assemble_circuit(
             # measurement result may be needed for a conditional gate.
             if instruction.name == "measure" and is_conditional_experiment:
                 instruction.register = clbit_indices
+        if op_context[0].definition is not None and op_context[0].definition.global_phase:
+            # pylint:  disable=no-member
+            header.global_phase += float(op_context[0].definition.global_phase)
 
         # To convert to a qobj-style conditional, insert a bfunc prior
         # to the conditional instruction to map the creg ?= val condition
diff --git a/qiskit/dagcircuit/dagcircuit.py b/qiskit/dagcircuit/dagcircuit.py
index 623291cd37ca..d943ff2d87c4 100644
--- a/qiskit/dagcircuit/dagcircuit.py
+++ b/qiskit/dagcircuit/dagcircuit.py
@@ -321,6 +321,19 @@ def _add_op_node(self, op, qargs, cargs):
         new_node._node_id = node_index
         return node_index
 
+    def _copy_circuit_metadata(self):
+        """Return a copy of source_dag with metadata but empty."""
+        target_dag = DAGCircuit()
+        target_dag.name = self.name
+        target_dag._global_phase = self._global_phase
+
+        for qreg in self.qregs.values():
+            target_dag.add_qreg(qreg)
+        for creg in self.cregs.values():
+            target_dag.add_creg(creg)
+
+        return target_dag
+
     def apply_operation_back(self, op, qargs=None, cargs=None, condition=None):
         """Apply an operation to the output of the circuit.
 
@@ -883,6 +896,9 @@ def substitute_node_with_dag(self, node, input_dag, wires=None):
                 in_dag.apply_operation_back(replay_node.op, replay_node.qargs,
                                             replay_node.cargs)
 
+        if in_dag.global_phase:
+            self.global_phase += in_dag.global_phase
+
         if wires is None:
             wires = in_dag.wires
 
diff --git a/qiskit/providers/basicaer/qasm_simulator.py b/qiskit/providers/basicaer/qasm_simulator.py
index 1a3c991adf23..6d0f25dc8781 100644
--- a/qiskit/providers/basicaer/qasm_simulator.py
+++ b/qiskit/providers/basicaer/qasm_simulator.py
@@ -456,6 +456,7 @@ def run_experiment(self, experiment):
         self._classical_memory = 0
         self._classical_register = 0
         self._sample_measure = False
+        global_phase = experiment.header.global_phase
         # Validate the dimension of initial statevector if set
         self._validate_initial_statevector()
         # Get the seed looking in circuit, qobj, and then random.
@@ -485,6 +486,8 @@ def run_experiment(self, experiment):
             shots = self._shots
         for _ in range(shots):
             self._initialize_statevector()
+            # apply global_phase
+            self._statevector *= np.exp(1j * global_phase)
             # Initialize classical memory to all 0
             self._classical_memory = 0
             self._classical_register = 0
diff --git a/qiskit/providers/basicaer/unitary_simulator.py b/qiskit/providers/basicaer/unitary_simulator.py
index 37cbddce5671..b38aa11370eb 100644
--- a/qiskit/providers/basicaer/unitary_simulator.py
+++ b/qiskit/providers/basicaer/unitary_simulator.py
@@ -116,6 +116,7 @@ def __init__(self, configuration=None, provider=None):
         self._number_of_qubits = 0
         self._initial_unitary = None
         self._chop_threshold = 1e-15
+        self._global_phase = 0
 
     def _add_unitary(self, gate, qubits):
         """Apply an N-qubit unitary matrix.
@@ -200,6 +201,8 @@ def _initialize_unitary(self):
     def _get_unitary(self):
         """Return the current unitary"""
         unitary = np.reshape(self._unitary, 2 * [2 ** self._number_of_qubits])
+        if self._global_phase:
+            unitary *= np.exp(1j * float(self._global_phase))
         unitary[abs(unitary) < self._chop_threshold] = 0.0
         return unitary
 
@@ -302,6 +305,7 @@ def run_experiment(self, experiment):
         """
         start = time.time()
         self._number_of_qubits = experiment.header.n_qubits
+        self._global_phase = experiment.header.global_phase
 
         # Validate the dimension of initial unitary if set
         self._validate_initial_unitary()
diff --git a/qiskit/transpiler/passes/basis/basis_translator.py b/qiskit/transpiler/passes/basis/basis_translator.py
index 5f322e012fab..752fabc29d7d 100644
--- a/qiskit/transpiler/passes/basis/basis_translator.py
+++ b/qiskit/transpiler/passes/basis/basis_translator.py
@@ -159,10 +159,12 @@ def run(self, dag):
                     bound_target_dag = circuit_to_dag(target_circuit)
                 else:
                     bound_target_dag = target_dag
-
+                if bound_target_dag.global_phase:
+                    dag.global_phase += bound_target_dag.global_phase
                 if (len(bound_target_dag.op_nodes()) == 1
                         and len(bound_target_dag.op_nodes()[0].qargs) == len(node.qargs)):
-                    dag.substitute_node(node, bound_target_dag.op_nodes()[0].op, inplace=True)
+                    dag_op = bound_target_dag.op_nodes()[0].op
+                    dag.substitute_node(node, dag_op, inplace=True)
                 else:
                     dag.substitute_node_with_dag(node, bound_target_dag)
             else:
diff --git a/qiskit/transpiler/passes/basis/decompose.py b/qiskit/transpiler/passes/basis/decompose.py
index 4627764233b9..444d73268b6b 100644
--- a/qiskit/transpiler/passes/basis/decompose.py
+++ b/qiskit/transpiler/passes/basis/decompose.py
@@ -46,6 +46,8 @@ def run(self, dag: DAGCircuit) -> DAGCircuit:
             # opaque or built-in gates are not decomposable
             if not node.op.definition:
                 continue
+            if node.op.definition.global_phase:
+                dag.global_phase += node.op.definition.global_phase
             # TODO: allow choosing among multiple decomposition rules
             rule = node.op.definition.data
 
diff --git a/qiskit/transpiler/passes/layout/apply_layout.py b/qiskit/transpiler/passes/layout/apply_layout.py
index 6a9e6bb27b44..97c9abf6a75d 100644
--- a/qiskit/transpiler/passes/layout/apply_layout.py
+++ b/qiskit/transpiler/passes/layout/apply_layout.py
@@ -57,5 +57,6 @@ def run(self, dag):
             if node.type == 'op':
                 qargs = [q[layout[qarg]] for qarg in node.qargs]
                 new_dag.apply_operation_back(node.op, qargs, node.cargs)
+        new_dag._global_phase = dag._global_phase
 
         return new_dag
diff --git a/qiskit/transpiler/passes/optimization/consolidate_blocks.py b/qiskit/transpiler/passes/optimization/consolidate_blocks.py
index 4ca44f2be771..cf904dedbf68 100644
--- a/qiskit/transpiler/passes/optimization/consolidate_blocks.py
+++ b/qiskit/transpiler/passes/optimization/consolidate_blocks.py
@@ -16,7 +16,6 @@
 
 
 from qiskit.circuit import QuantumRegister, ClassicalRegister, QuantumCircuit
-from qiskit.dagcircuit import DAGCircuit
 from qiskit.quantum_info.operators import Operator
 from qiskit.quantum_info.synthesis import TwoQubitBasisDecomposer
 from qiskit.extensions import UnitaryGate
@@ -75,11 +74,7 @@ def run(self, dag):
         if self.decomposer is None:
             return dag
 
-        new_dag = DAGCircuit()
-        for qreg in dag.qregs.values():
-            new_dag.add_qreg(qreg)
-        for creg in dag.cregs.values():
-            new_dag.add_creg(creg)
+        new_dag = dag._copy_circuit_metadata()
 
         # compute ordered indices for the global circuit wires
         global_index_map = {wire: idx for idx, wire in enumerate(dag.qubits)}
diff --git a/qiskit/transpiler/passes/optimization/optimize_1q_gates.py b/qiskit/transpiler/passes/optimization/optimize_1q_gates.py
index 61fbc38933e7..0b6bb8af831a 100644
--- a/qiskit/transpiler/passes/optimization/optimize_1q_gates.py
+++ b/qiskit/transpiler/passes/optimization/optimize_1q_gates.py
@@ -60,7 +60,7 @@ def run(self, dag):
         for run in runs:
             right_name = "u1"
             right_parameters = (0, 0, 0)  # (theta, phi, lambda)
-
+            right_global_phase = 0
             for current_node in run:
                 left_name = current_node.name
                 if (current_node.condition is not None
@@ -77,6 +77,9 @@ def run(self, dag):
                 else:
                     left_name = "u1"  # replace id with u1
                     left_parameters = (0, 0, 0)
+                if (current_node.op.definition is not None and
+                        current_node.op.definition.global_phase):
+                    right_global_phase += current_node.op.definition.global_phase
                 # If there are any sympy objects coming from the gate convert
                 # to numpy.
                 left_parameters = tuple([float(x) for x in left_parameters])
@@ -206,6 +209,8 @@ def run(self, dag):
                 else:
                     raise TranspilerError('It was not possible to use the basis %s' % self.basis)
 
+            dag.global_phase += right_global_phase
+
             if right_name != 'nop':
                 dag.substitute_node(run[0], new_op, inplace=True)
 
diff --git a/qiskit/transpiler/passes/routing/basic_swap.py b/qiskit/transpiler/passes/routing/basic_swap.py
index 8eb49b0e4eff..2641163d0d84 100644
--- a/qiskit/transpiler/passes/routing/basic_swap.py
+++ b/qiskit/transpiler/passes/routing/basic_swap.py
@@ -49,11 +49,7 @@ def run(self, dag):
             TranspilerError: if the coupling map or the layout are not
             compatible with the DAG.
         """
-        new_dag = DAGCircuit()
-        for qreg in dag.qregs.values():
-            new_dag.add_qreg(qreg)
-        for creg in dag.cregs.values():
-            new_dag.add_creg(creg)
+        new_dag = dag._copy_circuit_metadata()
 
         if len(dag.qregs) != 1 or dag.qregs.get('q', None) is None:
             raise TranspilerError('Basic swap runs on physical circuits only')
diff --git a/qiskit/transpiler/passes/routing/sabre_swap.py b/qiskit/transpiler/passes/routing/sabre_swap.py
index 32ac0de6d219..59954b86bf88 100644
--- a/qiskit/transpiler/passes/routing/sabre_swap.py
+++ b/qiskit/transpiler/passes/routing/sabre_swap.py
@@ -17,7 +17,6 @@
 from itertools import cycle
 import numpy as np
 
-from qiskit.dagcircuit import DAGCircuit
 from qiskit.circuit.library.standard_gates import SwapGate
 from qiskit.transpiler.basepasses import TransformationPass
 from qiskit.transpiler.exceptions import TranspilerError
@@ -145,7 +144,7 @@ def run(self, dag):
         rng = np.random.default_rng(self.seed)
 
         # Preserve input DAG's name, regs, wire_map, etc. but replace the graph.
-        mapped_dag = _copy_circuit_metadata(dag)
+        mapped_dag = dag._copy_circuit_metadata()
 
         # Assume bidirectional couplings, fixing gate direction is easy later.
         self.coupling_map.make_symmetric()
@@ -335,20 +334,6 @@ def _score_heuristic(self, heuristic, front_layer, extended_set, layout, swap_qu
             raise TranspilerError('Heuristic %s not recognized.' % heuristic)
 
 
-def _copy_circuit_metadata(source_dag):
-    """Return a copy of source_dag with metadata but empty.
-    """
-    target_dag = DAGCircuit()
-    target_dag.name = source_dag.name
-
-    for qreg in source_dag.qregs.values():
-        target_dag.add_qreg(qreg)
-    for creg in source_dag.cregs.values():
-        target_dag.add_creg(creg)
-
-    return target_dag
-
-
 def _transform_gate_for_layout(op_node, layout):
     """Return node implementing a virtual op on given layout."""
     mapped_op_node = deepcopy(op_node)
diff --git a/qiskit/transpiler/passes/routing/stochastic_swap.py b/qiskit/transpiler/passes/routing/stochastic_swap.py
index be98d51b72a4..095a0bd2723f 100644
--- a/qiskit/transpiler/passes/routing/stochastic_swap.py
+++ b/qiskit/transpiler/passes/routing/stochastic_swap.py
@@ -299,12 +299,7 @@ def _mapper(self, circuit_graph, coupling_graph, trials=20):
 
         # Construct an empty DAGCircuit with the same set of
         # qregs and cregs as the input circuit
-        dagcircuit_output = DAGCircuit()
-        dagcircuit_output.name = circuit_graph.name
-        for qreg in circuit_graph.qregs.values():
-            dagcircuit_output.add_qreg(qreg)
-        for creg in circuit_graph.cregs.values():
-            dagcircuit_output.add_creg(creg)
+        dagcircuit_output = circuit_graph._copy_circuit_metadata()
 
         logger.debug("trivial_layout = %s", layout)
 
diff --git a/qiskit/transpiler/passes/utils/merge_adjacent_barriers.py b/qiskit/transpiler/passes/utils/merge_adjacent_barriers.py
index 93fa091b6958..56310311af07 100644
--- a/qiskit/transpiler/passes/utils/merge_adjacent_barriers.py
+++ b/qiskit/transpiler/passes/utils/merge_adjacent_barriers.py
@@ -13,7 +13,6 @@
 """Return a circuit with any adjacent barriers merged together."""
 
 from qiskit.transpiler.basepasses import TransformationPass
-from qiskit.dagcircuit import DAGCircuit
 from qiskit.circuit.barrier import Barrier
 
 
@@ -59,12 +58,7 @@ def run(self, dag):
             return dag
 
         # add the merged barriers to a new DAG
-        new_dag = DAGCircuit()
-
-        for qreg in dag.qregs.values():
-            new_dag.add_qreg(qreg)
-        for creg in dag.cregs.values():
-            new_dag.add_creg(creg)
+        new_dag = dag._copy_circuit_metadata()
 
         # go over current nodes, and add them to the new dag
         for node in dag.topological_op_nodes():
diff --git a/qiskit/transpiler/passes/utils/remove_final_measurements.py b/qiskit/transpiler/passes/utils/remove_final_measurements.py
index 8c755cd47622..377ba784946d 100644
--- a/qiskit/transpiler/passes/utils/remove_final_measurements.py
+++ b/qiskit/transpiler/passes/utils/remove_final_measurements.py
@@ -13,7 +13,6 @@
 """Remove final measurements and barriers at the end of a circuit."""
 
 from qiskit.transpiler.basepasses import TransformationPass
-from qiskit.dagcircuit import DAGCircuit
 
 
 class RemoveFinalMeasurements(TransformationPass):
@@ -54,8 +53,6 @@ def run(self, dag):
         if not final_ops:
             return dag
 
-        new_dag = DAGCircuit()
-
         for node in final_ops:
             for carg in node.cargs:
                 # Add the clbit that was attached to the measure we are removing
@@ -75,11 +72,7 @@ def run(self, dag):
             if val in cregs_to_remove and cregs_to_remove[val] == val.size:
                 del dag.cregs[key]
 
-        # Fill new DAGCircuit
-        for qreg in dag.qregs.values():
-            new_dag.add_qreg(qreg)
-        for creg in dag.cregs.values():
-            new_dag.add_creg(creg)
+        new_dag = dag._copy_circuit_metadata()
 
         for node in dag.topological_op_nodes():
             # copy the condition over too
diff --git a/test/python/basicaer/test_statevector_simulator.py b/test/python/basicaer/test_statevector_simulator.py
index afa47d1e4805..8ae9ae915e84 100644
--- a/test/python/basicaer/test_statevector_simulator.py
+++ b/test/python/basicaer/test_statevector_simulator.py
@@ -83,6 +83,37 @@ def test_unitary(self):
                 fidelity = state_fidelity(psi_target, psi_out)
                 self.assertGreater(fidelity, 0.999)
 
+    def test_global_phase(self):
+        """Test global_phase"""
+        n_qubits = 4
+        qr = QuantumRegister(n_qubits)
+        circ = QuantumCircuit(qr)
+        circ.x(qr)
+        circ.global_phase = 0.5
+        self.circuit = circ
+        result = super().test_run_circuit()
+        actual = result.get_statevector(self.circuit)
+        expected = np.exp(1j * circ.global_phase) * np.repeat([[0], [1]], [n_qubits**2-1, 1])
+        self.assertTrue(np.allclose(actual, expected))
+
+    def test_global_phase_composite(self):
+        """Test global_phase"""
+        n_qubits = 4
+        qr = QuantumRegister(n_qubits)
+        circ = QuantumCircuit(qr)
+        circ.x(qr)
+        circ.global_phase = 0.5
+        gate = circ.to_gate()
+
+        comp = QuantumCircuit(qr)
+        comp.append(gate, qr)
+        comp.global_phase = 0.1
+        self.circuit = comp
+        result = super().test_run_circuit()
+        actual = result.get_statevector(self.circuit)
+        expected = np.exp(1j * 0.6) * np.repeat([[0], [1]], [n_qubits**2-1, 1])
+        self.assertTrue(np.allclose(actual, expected))
+
 
 if __name__ == '__main__':
     unittest.main()
diff --git a/test/python/circuit/test_controlled_gate.py b/test/python/circuit/test_controlled_gate.py
index 2161bf45f7f7..e8615a885227 100644
--- a/test/python/circuit/test_controlled_gate.py
+++ b/test/python/circuit/test_controlled_gate.py
@@ -658,6 +658,15 @@ def test_open_controlled_unitary_z(self, num_ctrl_qubits, ctrl_state):
         ref_mat = _compute_control_matrix(umat, num_ctrl_qubits, ctrl_state=ctrl_state)
         self.assertEqual(Operator(cugate), Operator(ref_mat))
 
+    def test_controlled_controlled_rz(self):
+        """Test that UnitaryGate with control returns params."""
+        qc = QuantumCircuit(1)
+        qc.rz(0.2, 0)
+        controlled = QuantumCircuit(2)
+        controlled.compose(qc.control(), inplace=True)
+        self.assertEqual(Operator(controlled), Operator(CRZGate(0.2)))
+        self.assertEqual(Operator(controlled), Operator(RZGate(0.2).control()))
+
     def test_controlled_controlled_unitary(self):
         """Test that global phase in iso decomposition of unitary is handled."""
         umat = np.array([[1, 0], [0, -1]])
diff --git a/test/python/circuit/test_extensions_standard.py b/test/python/circuit/test_extensions_standard.py
index aab7b5ffd2a7..14a64f0acc7e 100644
--- a/test/python/circuit/test_extensions_standard.py
+++ b/test/python/circuit/test_extensions_standard.py
@@ -1381,7 +1381,7 @@ def test_to_matrix_op(self):
         from qiskit.quantum_info import Operator
         from qiskit.circuit.library.standard_gates.ms import MSGate
 
-        params = [0.1 * i for i in range(10)]
+        params = [0.1 * i for i in range(1, 11)]
         gate_class_list = Gate.__subclasses__() + ControlledGate.__subclasses__()
         for gate_class in gate_class_list:
             sig = signature(gate_class)
diff --git a/test/python/transpiler/test_basis_translator.py b/test/python/transpiler/test_basis_translator.py
index 5709f0a831c8..dcdf7325145e 100644
--- a/test/python/transpiler/test_basis_translator.py
+++ b/test/python/transpiler/test_basis_translator.py
@@ -643,3 +643,21 @@ def test_cx_bell_to_iswap(self):
         expected_dag = circuit_to_dag(expected)
 
         self.assertEqual(out_dag, expected_dag)
+
+    def test_global_phase(self):
+        """Verify global phase preserved in basis translation"""
+        circ = QuantumCircuit(1)
+        gate_angle = pi / 5
+        circ_angle = pi / 3
+        circ.rz(gate_angle, 0)
+        circ.global_phase = circ_angle
+        in_dag = circuit_to_dag(circ)
+        out_dag = BasisTranslator(std_eqlib, ['u1']).run(in_dag)
+
+        qr = QuantumRegister(1, 'q')
+        expected = QuantumCircuit(qr)
+        expected.u1(gate_angle, qr)
+        expected.global_phase = circ_angle - gate_angle / 2
+        expected_dag = circuit_to_dag(expected)
+        self.assertEqual(out_dag, expected_dag)
+        self.assertEqual(float(out_dag.global_phase), float(expected_dag.global_phase))
diff --git a/test/python/transpiler/test_decompose.py b/test/python/transpiler/test_decompose.py
index 4899e7dee02c..7950f50c97cc 100644
--- a/test/python/transpiler/test_decompose.py
+++ b/test/python/transpiler/test_decompose.py
@@ -19,6 +19,7 @@
 from qiskit.converters import circuit_to_dag
 from qiskit.circuit.library import HGate
 from qiskit.circuit.library import CCXGate
+from qiskit.quantum_info.operators import Operator
 from qiskit.test import QiskitTestCase
 
 
@@ -100,3 +101,20 @@ def test_decompose_oversized_instruction(self):
         output = qc2.decompose()
 
         self.assertEqual(qc1, output)
+
+    def test_decompose_global_phase_1q(self):
+        """Test decomposition of circuit with global phase"""
+        qc = QuantumCircuit(1)
+        qc.rz(0.1, 0)
+        qc.ry(0.5, 0)
+        qc.global_phase += pi/4
+        qcd = qc.decompose()
+        self.assertEqual(Operator(qc), Operator(qcd))
+
+    def test_decompose_global_phase_2q(self):
+        """Test decomposition of circuit with global phase"""
+        qc = QuantumCircuit(2, global_phase=pi/4)
+        qc.rz(0.1, 0)
+        qc.rxx(0.2, 0, 1)
+        qcd = qc.decompose()
+        self.assertEqual(Operator(qc), Operator(qcd))
diff --git a/test/python/transpiler/test_optimize_1q_gates.py b/test/python/transpiler/test_optimize_1q_gates.py
index 3944643bfefb..4d8d010f5012 100644
--- a/test/python/transpiler/test_optimize_1q_gates.py
+++ b/test/python/transpiler/test_optimize_1q_gates.py
@@ -221,6 +221,21 @@ def test_parameterized_expressions_in_circuits(self):
 
         self.assertEqual(circuit_to_dag(expected), after)
 
+    def test_global_phase_u3_on_left(self):
+        """Check proper phase accumulation with instruction with no definition."""
+        from qiskit.circuit.library.standard_gates import U1Gate
+        qr = QuantumRegister(1)
+        qc = QuantumCircuit(qr)
+        u1 = U1Gate(0.1)
+        u1.definition.global_phase = np.pi / 2
+        qc.append(u1, [0])
+        qc.global_phase = np.pi / 3
+        qc.u3(0.1, 0.2, 0.3, 0)
+
+        dag = circuit_to_dag(qc)
+        after = Optimize1qGates().run(dag)
+        self.assertAlmostEqual(after.global_phase, 5 * np.pi / 6, 8)
+
 
 class TestOptimize1qGatesParamReduction(QiskitTestCase):
     """Test for 1q gate optimizations parameter reduction, reduce n in Un """