diff --git a/docs/markdown/Syntax.md b/docs/markdown/Syntax.md
index f4a2e1772a2a..21e73cbb21e9 100644
--- a/docs/markdown/Syntax.md
+++ b/docs/markdown/Syntax.md
@@ -80,6 +80,15 @@ string_var = '42'
 num = string_var.to_int()
 ```
 
+Hexadecimal, octal, and binary strings can be converted to numbers since
+1.10.0:
+
+```meson
+hex_var = '0xFF'.to_int()    # 255
+oct_var = '0o755'.to_int()   # 493
+bin_var = '0b1010'.to_int()  # 10
+```
+
 Numbers can be converted to a string:
 
 ```meson
@@ -87,6 +96,15 @@ int_var = 42
 string_var = int_var.to_string()
 ```
 
+Numbers can be formatted as hexadecimal, octal, or binary strings since 1.10.0:
+
+```meson
+int_var = 255
+hex_str = int_var.to_string(format: 'hex')  # '0xff'
+oct_str = int_var.to_string(format: 'oct')  # '0o377'
+bin_str = int_var.to_string(format: 'bin')  # '0b11111111'
+```
+
 ## Booleans
 
 A boolean is either `true` or `false`.
diff --git a/mesonbuild/interpreter/primitives/integer.py b/mesonbuild/interpreter/primitives/integer.py
index c59ea6e229a3..1ef5c6584fb3 100644
--- a/mesonbuild/interpreter/primitives/integer.py
+++ b/mesonbuild/interpreter/primitives/integer.py
@@ -7,12 +7,20 @@
     FeatureBroken, InvalidArguments, KwargInfo,
     noKwargs, noPosargs, typed_operator, typed_kwargs
 )
+from ..type_checking import in_set_validator
 
 import typing as T
 
 if T.TYPE_CHECKING:
+    from typing_extensions import Literal, TypedDict
+
     from ...interpreterbase import TYPE_var, TYPE_kwargs
 
+    class ToStringKw(TypedDict):
+
+        fill: int
+        format: Literal["dec", "hex", "oct", "bin"]
+
 class IntegerHolder(ObjectHolder[int]):
     # Operators that only require type checks
     TRIVIAL_OPERATORS = {
@@ -55,12 +63,20 @@ def is_odd_method(self, args: T.List[TYPE_var], kwargs: TYPE_kwargs) -> bool:
 
     @typed_kwargs(
         'to_string',
-        KwargInfo('fill', int, default=0, since='1.3.0')
+        KwargInfo('fill', int, default=0, since='1.3.0'),
+        KwargInfo(
+            "format",
+            str,
+            default="dec",
+            since="1.10.0",
+            validator=in_set_validator({"dec", "hex", "oct", "bin"}),
+        ),
     )
     @noPosargs
     @InterpreterObject.method('to_string')
-    def to_string_method(self, args: T.List[TYPE_var], kwargs: T.Dict[str, T.Any]) -> str:
-        return str(self.held_object).zfill(kwargs['fill'])
+    def to_string_method(self, args: T.List[TYPE_var], kwargs: 'ToStringKw') -> str:
+        format_codes = {"hex": "x", "oct": "o", "bin": "b", "dec": "d"}
+        return format(self.held_object, f'#0{kwargs["fill"]}{format_codes[kwargs["format"]]}')
 
     @typed_operator(MesonOperator.DIV, int)
     @InterpreterObject.operator(MesonOperator.DIV)
diff --git a/mesonbuild/interpreter/primitives/string.py b/mesonbuild/interpreter/primitives/string.py
index 190e82a39559..d780ec851679 100644
--- a/mesonbuild/interpreter/primitives/string.py
+++ b/mesonbuild/interpreter/primitives/string.py
@@ -132,7 +132,19 @@ def substring_method(self, args: T.Tuple[T.Optional[int], T.Optional[int]], kwar
     @InterpreterObject.method('to_int')
     def to_int_method(self, args: T.List[TYPE_var], kwargs: TYPE_kwargs) -> int:
         try:
-            return int(self.held_object)
+            s = self.held_object.strip()
+            s_unsigned = s.lstrip('+-').lower()
+
+            if s_unsigned.startswith('0x'):
+                base = 16
+            elif s_unsigned.startswith('0o'):
+                base = 8
+            elif s_unsigned.startswith('0b'):
+                base = 2
+            else:
+                base = 10
+
+            return int(s, base)
         except ValueError:
             raise InvalidArguments(f'String {self.held_object!r} cannot be converted to int')
 
diff --git a/test cases/common/286 number base conversions/meson.build b/test cases/common/286 number base conversions/meson.build
new file mode 100644
index 000000000000..42811f6759fa
--- /dev/null
+++ b/test cases/common/286 number base conversions/meson.build	
@@ -0,0 +1,131 @@
+project('test number base conversions')
+
+### .to_int()
+
+# hexadecimal strings
+assert('0x10'.to_int() == 16, 'Hex string conversion failed')
+assert('0X10'.to_int() == 16, 'Hex string conversion (uppercase X) failed')
+assert('0xff'.to_int() == 255, 'Hex string conversion (lowercase) failed')
+assert('0xFF'.to_int() == 255, 'Hex string conversion (uppercase) failed')
+assert('0xDEADBEEF'.to_int() == 3735928559, 'Large hex conversion failed')
+assert('0x1'.to_int() == 1, 'Small hex conversion failed')
+assert('0x0'.to_int() == 0, 'Zero hex conversion failed')
+
+# signed hexadecimal strings
+assert('-0xf'.to_int() == -15, 'Negative hex string conversion failed')
+assert('+0x10'.to_int() == 16, 'Positive hex string conversion failed')
+assert('-0xFF'.to_int() == -255, 'Negative hex string (uppercase) conversion failed')
+
+# octal strings
+assert('0o10'.to_int() == 8, 'Octal string conversion failed')
+assert('0O10'.to_int() == 8, 'Octal string conversion (uppercase O) failed')
+assert('0o77'.to_int() == 63, 'Octal string conversion failed')
+assert('0o755'.to_int() == 493, 'Octal permission-like conversion failed')
+assert('0o0'.to_int() == 0, 'Zero octal conversion failed')
+
+# signed octal strings
+assert('-0o10'.to_int() == -8, 'Negative octal string conversion failed')
+assert('+0o77'.to_int() == 63, 'Positive octal string conversion failed')
+
+# binary strings
+assert('0b10'.to_int() == 2, 'Binary string conversion failed')
+assert('0B10'.to_int() == 2, 'Binary string conversion (uppercase B) failed')
+assert('0b1111'.to_int() == 15, 'Binary string conversion failed')
+assert('0b11111111'.to_int() == 255, 'Binary byte conversion failed')
+assert('0b0'.to_int() == 0, 'Zero binary conversion failed')
+
+# signed binary strings
+assert('-0b101'.to_int() == -5, 'Negative binary string conversion failed')
+assert('+0b1111'.to_int() == 15, 'Positive binary string conversion failed')
+
+# decimal strings (backwards compat)
+assert('10'.to_int() == 10, 'Decimal string conversion failed')
+assert('255'.to_int() == 255, 'Decimal string conversion failed')
+assert('0'.to_int() == 0, 'Zero decimal conversion failed')
+assert('12345'.to_int() == 12345, 'Large decimal conversion failed')
+
+# leading zeroes are decimal (backwards compat)
+assert('010'.to_int() == 10, 'Decimal with leading zero broke backward compatibility')
+assert('0123'.to_int() == 123, 'Decimal with leading zeros broke backward compatibility')
+assert('007'.to_int() == 7, 'Decimal with leading zeros broke backward compatibility')
+
+### .to_string()
+
+# hex format
+assert(16.to_string(format: 'hex') == '0x10', 'Int to hex string failed')
+assert(255.to_string(format: 'hex') == '0xff', 'Int to hex string failed')
+assert(0.to_string(format: 'hex') == '0x0', 'Zero to hex string failed')
+assert(1.to_string(format: 'hex') == '0x1', 'One to hex string failed')
+assert(3735928559.to_string(format: 'hex') == '0xdeadbeef', 'Large hex string failed')
+
+# octal format
+assert(8.to_string(format: 'oct') == '0o10', 'Int to octal string failed')
+assert(63.to_string(format: 'oct') == '0o77', 'Int to octal string failed')
+assert(493.to_string(format: 'oct') == '0o755', 'Permission to octal string failed')
+assert(0.to_string(format: 'oct') == '0o0', 'Zero to octal string failed')
+
+# binary format
+assert(2.to_string(format: 'bin') == '0b10', 'Int to binary string failed')
+assert(15.to_string(format: 'bin') == '0b1111', 'Int to binary string failed')
+assert(255.to_string(format: 'bin') == '0b11111111', 'Byte to binary string failed')
+assert(0.to_string(format: 'bin') == '0b0', 'Zero to binary string failed')
+
+# decimal format (explicit)
+assert(10.to_string(format: 'dec') == '10', 'Int to decimal string failed')
+assert(255.to_string(format: 'dec') == '255', 'Int to decimal string failed')
+
+# default
+assert(42.to_string() == '42', 'Default int to string failed')
+
+# fill and hex format
+assert(255.to_string(format: 'hex', fill: 8) == '0x0000ff', 'Hex with fill failed')
+assert(1.to_string(format: 'hex', fill: 6) == '0x0001', 'Hex with fill failed')
+assert(255.to_string(format: 'hex', fill: 4) == '0xff', 'Hex with fill (no padding needed) failed')
+
+# fill and other formats
+assert(8.to_string(format: 'oct', fill: 6) == '0o0010', 'Octal with fill failed')
+assert(2.to_string(format: 'bin', fill: 10) == '0b00000010', 'Binary with fill failed')
+
+# negative numbers
+assert((-15).to_string(format: 'hex') == '-0xf', 'Negative hex conversion failed')
+assert((-8).to_string(format: 'oct') == '-0o10', 'Negative octal conversion failed')
+assert((-5).to_string(format: 'bin') == '-0b101', 'Negative binary conversion failed')
+
+# negative numbers and fill
+assert((-15).to_string(format: 'hex', fill: 6) == '-0x00f', 'Negative hex with fill failed')
+assert((-8).to_string(format: 'oct', fill: 7) == '-0o0010', 'Negative octal with fill failed')
+assert((-5).to_string(format: 'bin', fill: 8) == '-0b00101', 'Negative binary with fill failed')
+assert((-4).to_string(fill: 3) == '-04', 'Negative decimal with fill failed')
+
+# fill and decimal
+assert(4.to_string(fill: 3) == '004', 'Decimal with fill failed')
+
+### Round trip conversions
+
+# positive
+
+hex_val = 0x200
+hex_str = hex_val.to_string(format: 'hex')
+assert(hex_str.to_int() == hex_val, 'Hex round-trip failed')
+
+oct_val = 0o755
+oct_str = oct_val.to_string(format: 'oct')
+assert(oct_str.to_int() == oct_val, 'Octal round-trip failed')
+
+bin_val = 0b11010
+bin_str = bin_val.to_string(format: 'bin')
+assert(bin_str.to_int() == bin_val, 'Binary round-trip failed')
+
+# negative
+
+neg_hex = -255
+neg_hex_str = neg_hex.to_string(format: 'hex')
+assert(neg_hex_str.to_int() == neg_hex, 'Negative hex round-trip failed')
+
+neg_oct = -63
+neg_oct_str = neg_oct.to_string(format: 'oct')
+assert(neg_oct_str.to_int() == neg_oct, 'Negative octal round-trip failed')
+
+neg_bin = -15
+neg_bin_str = neg_bin.to_string(format: 'bin')
+assert(neg_bin_str.to_int() == neg_bin, 'Negative binary round-trip failed')
diff --git a/test cases/common/35 string operations/meson.build b/test cases/common/35 string operations/meson.build
index 8cc5b0c08f61..6d3993bfce51 100644
--- a/test cases/common/35 string operations/meson.build	
+++ b/test cases/common/35 string operations/meson.build	
@@ -54,6 +54,9 @@ assert('#include <foo/bar.h>'.underscorify() == '_include__foo_bar_h_', 'Broken
 assert('Do SomeThing 09'.underscorify() == 'Do_SomeThing_09', 'Broken underscorify')
 
 assert('3'.to_int() == 3, 'String int conversion does not work.')
+assert('0x10'.to_int() == 16, 'Hex string conversion does not work.')
+assert('0o10'.to_int() == 8, 'Octal string conversion does not work.')
+assert('0b10'.to_int() == 2, 'Binary string conversion does not work.')
 
 assert(true.to_string() == 'true', 'bool string conversion failed')
 assert(false.to_string() == 'false', 'bool string conversion failed')