diff --git a/base/broadcast.jl b/base/broadcast.jl
index b55051d82546d..34c2241864fd6 100644
--- a/base/broadcast.jl
+++ b/base/broadcast.jl
@@ -8,7 +8,7 @@ Module containing the broadcasting implementation.
 module Broadcast
 
 using .Base.Cartesian
-using .Base: Indices, OneTo, tail, to_shape, isoperator, promote_typejoin,
+using .Base: Indices, OneTo, tail, to_shape, isoperator, promote_typejoin, @pure,
              _msk_end, unsafe_bitgetindex, bitcache_chunks, bitcache_size, dumpbitcache, unalias
 import .Base: copy, copyto!, axes
 export broadcast, broadcast!, BroadcastStyle, broadcast_axes, broadcastable, dotview, @__dot__, broadcast_preserving_zero_d, BroadcastFunction
@@ -691,8 +691,52 @@ eltypes(t::Tuple{Any}) = Tuple{_broadcast_getindex_eltype(t[1])}
 eltypes(t::Tuple{Any,Any}) = Tuple{_broadcast_getindex_eltype(t[1]), _broadcast_getindex_eltype(t[2])}
 eltypes(t::Tuple) = Tuple{_broadcast_getindex_eltype(t[1]), eltypes(tail(t)).types...}
 
+function promote_typejoin_union(::Type{T}) where T
+    if T === Union{}
+        return Union{}
+    elseif T isa Union
+        return promote_typejoin(promote_typejoin_union(T.a), promote_typejoin_union(T.b))
+    elseif T <: Tuple
+        return typejoin_union_tuple(T)
+    else
+        return T
+    end
+end
+
+@pure function typejoin_union_tuple(T::Type)
+    u = Base.unwrap_unionall(T)
+    u isa Union && return typejoin(
+            typejoin_union_tuple(Base.rewrap_unionall(u.a, T)),
+            typejoin_union_tuple(Base.rewrap_unionall(u.b, T)))
+    p = (u::DataType).parameters
+    lr = length(p)::Int
+    if lr == 0
+        return Tuple{}
+    end
+    c = Vector{Any}(undef, lr)
+    for i = 1:lr
+        pi = p[i]
+        U = Core.Compiler.unwrapva(pi)
+        if U === Union{}
+            ci = Union{}
+        elseif U isa Union
+            ci = typejoin(U.a, U.b)
+        else
+            ci = U
+        end
+        if i == lr && Core.Compiler.isvarargtype(pi)
+            N = (Base.unwrap_unionall(pi)::DataType).parameters[2]
+            c[i] = Base.rewrap_unionall(Vararg{ci, N}, pi)
+        else
+            c[i] = ci
+        end
+    end
+    return Base.rewrap_unionall(Tuple{c...}, T)
+end
+
 # Inferred eltype of result of broadcast(f, args...)
-combine_eltypes(f, args::Tuple) = Base._return_type(f, eltypes(args))
+combine_eltypes(f, args::Tuple) =
+    promote_typejoin_union(Base._return_type(f, eltypes(args)))
 
 ## Broadcasting core
 
@@ -877,7 +921,11 @@ const NonleafHandlingStyles = Union{DefaultArrayStyle,ArrayConflict}
     dest = similar(bc′, typeof(val))
     @inbounds dest[I] = val
     # Now handle the remaining values
-    return copyto_nonleaf!(dest, bc′, iter, state, 1)
+    # The typeassert gives inference a helping hand on the element type and dimensionality
+    # (work-around for #28382)
+    ElType′ = ElType <: Type ? Type : ElType
+    RT = dest isa AbstractArray ? AbstractArray{<:ElType′, ndims(dest)} : Any
+    return copyto_nonleaf!(dest, bc′, iter, state, 1)::RT
 end
 
 ## general `copyto!` methods
diff --git a/test/broadcast.jl b/test/broadcast.jl
index 7fcc793fb6844..8a5b003fca8f3 100644
--- a/test/broadcast.jl
+++ b/test/broadcast.jl
@@ -365,7 +365,7 @@ end
 let f17314 = x -> x < 0 ? false : x
     @test eltype(broadcast(f17314, 1:3)) === Int
     @test eltype(broadcast(f17314, -1:1)) === Integer
-    @test eltype(broadcast(f17314, Int[])) == Union{Bool,Int}
+    @test eltype(broadcast(f17314, Int[])) === Integer
 end
 let io = IOBuffer()
     broadcast(x->print(io,x), 1:5) # broadcast with side effects
@@ -950,3 +950,41 @@ p0 = copy(p)
 @test map(.+, [[1,2], [3,4]], [5, 6]) == [[6,7], [9,10]]
 @test repr(.!) == "Base.Broadcast.BroadcastFunction(!)"
 @test eval(:(.+)) == Base.BroadcastFunction(+)
+
+@testset "Issue #28382: inferrability of broadcast with Union eltype" begin
+    @test isequal([1, 2] .+ [3.0, missing], [4.0, missing])
+    @test_broken Core.Compiler.return_type(broadcast, Tuple{typeof(+), Vector{Int},
+                                                            Vector{Union{Float64, Missing}}}) ==
+        Vector{<:Union{Float64, Missing}}
+    @test Core.Compiler.return_type(broadcast, Tuple{typeof(+), Vector{Int},
+                                                     Vector{Union{Float64, Missing}}}) ==
+        AbstractVector{<:Union{Float64, Missing}}
+    @test isequal([1, 2] + [3.0, missing], [4.0, missing])
+    @test_broken Core.Compiler.return_type(+, Tuple{Vector{Int},
+                                                    Vector{Union{Float64, Missing}}}) ==
+        Vector{<:Union{Float64, Missing}}
+    @test Core.Compiler.return_type(+, Tuple{Vector{Int},
+                                             Vector{Union{Float64, Missing}}}) ==
+        AbstractVector{<:Union{Float64, Missing}}
+    @test_broken Core.Compiler.return_type(+, Tuple{Vector{Int},
+                                                    Vector{Union{Float64, Missing}}}) ==
+        Vector{<:Union{Float64, Missing}}
+    @test isequal(tuple.([1, 2], [3.0, missing]), [(1, 3.0), (2, missing)])
+    @test_broken Core.Compiler.return_type(broadcast, Tuple{typeof(tuple), Vector{Int},
+                                                            Vector{Union{Float64, Missing}}}) ==
+        Vector{<:Tuple{Int, Any}}
+    @test Core.Compiler.return_type(broadcast, Tuple{typeof(tuple), Vector{Int},
+                                                     Vector{Union{Float64, Missing}}}) ==
+        AbstractVector{<:Tuple{Int, Any}}
+    # Check that corner cases do not throw an error
+    @test isequal(broadcast(x -> x === 1 ? nothing : x, [1, 2, missing]),
+                  [nothing, 2, missing])
+    @test isequal(broadcast(x -> x === 1 ? nothing : x, Any[1, 2, 3.0, missing]),
+                  [nothing, 2, 3, missing])
+    @test broadcast((x,y)->(x==1 ? 1.0 : x, y), [1 2 3], ["a", "b", "c"]) ==
+        [(1.0, "a") (2, "a") (3, "a")
+         (1.0, "b") (2, "b") (3, "b")
+         (1.0, "c") (2, "c") (3, "c")]
+    @test typeof.([iszero, isdigit]) == [typeof(iszero), typeof(isdigit)]
+    @test typeof.([iszero, iszero]) == [typeof(iszero), typeof(iszero)]
+end