diff --git a/base/tuple.jl b/base/tuple.jl
index b3799e57d6fba..3b45f812fc0b6 100644
--- a/base/tuple.jl
+++ b/base/tuple.jl
@@ -63,6 +63,16 @@ first(t::Tuple) = t[1]
 
 eltype(::Type{Tuple{}}) = Bottom
 eltype(::Type{<:Tuple{Vararg{E}}}) where {E} = E
+function eltype(t::Type{<:Tuple})
+    @_pure_meta
+    t isa Union && return typejoin(eltype(t.a), eltype(t.b))
+    t´ = unwrap_unionall(t)
+    r = Union{}
+    for ti in t´.parameters
+        r = typejoin(r, rewrap_unionall(unwrapva(ti), t))
+    end
+    return r
+end
 
 # version of tail that doesn't throw on empty tuples (used in array indexing)
 safe_tail(t::Tuple) = tail(t)
diff --git a/test/tuple.jl b/test/tuple.jl
index 20ccbe348587c..70f08a30f667a 100644
--- a/test/tuple.jl
+++ b/test/tuple.jl
@@ -65,8 +65,14 @@ end
 @test eltype((1,2,3)) === Int
 @test eltype((1.0,2.0,3.0)) <: AbstractFloat
 @test eltype((true, false)) === Bool
-@test eltype((1,2.0, false)) === Any
+@test eltype((1, 2.0, false)) === typejoin(Int, Float64, Bool)
 @test eltype(()) === Union{}
+@test eltype(Tuple{Int, Float64, Vararg{Bool}}) === typejoin(Int, Float64, Bool)
+@test eltype(Tuple{Int, T, Vararg{Bool}} where T <: AbstractFloat) ===
+    typejoin(Int, AbstractFloat, Bool)
+@test eltype(Tuple{Int, Bool, Vararg{T}} where T <: AbstractFloat) ===
+    typejoin(Int, AbstractFloat, Bool)
+@test eltype(Union{Tuple{Int, Float64}, Tuple{Vararg{Bool}}}) === typejoin(Int, Float64, Bool)
 
 begin
     local foo