diff --git a/NEWS.md b/NEWS.md
index d650733551474..dbacdc77229ec 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -10,6 +10,8 @@ New language features
 Language changes
 ----------------
 
+  * the constructor `BigFloat(::BigFloat)` now respects the global precision setting and always
+    returns a `BigFloat` with precision equal to `precision(BigFloat)` ([#29127]).
   * Parser inputs ending with a comma are now consistently treated as incomplete.
     Previously they were sometimes parsed as tuples, depending on whitespace ([#28506]).
 
diff --git a/base/mpfr.jl b/base/mpfr.jl
index 2d5acf2605d48..504d63ee59a1f 100644
--- a/base/mpfr.jl
+++ b/base/mpfr.jl
@@ -116,7 +116,17 @@ BigFloat(x)
 widen(::Type{Float64}) = BigFloat
 widen(::Type{BigFloat}) = BigFloat
 
-BigFloat(x::BigFloat) = x
+function BigFloat(x::BigFloat)
+    if precision(BigFloat) == precision(x)
+        x
+    else
+        z = BigFloat()
+        ccall((:mpfr_set, :libmpfr), Int32, (Ref{BigFloat}, Ref{BigFloat}, Int32),
+              z, x, ROUNDING_MODE[])
+        z
+    end
+end
+
 
 # convert to BigFloat
 for (fJ, fC) in ((:si,:Clong), (:ui,:Culong))
diff --git a/test/mpfr.jl b/test/mpfr.jl
index bfb16a6ce2995..3e69762caf081 100644
--- a/test/mpfr.jl
+++ b/test/mpfr.jl
@@ -35,6 +35,20 @@ import Base.MPFR
 
     @test typeof(BigFloat(1//1)) == BigFloat
     @test typeof(BigFloat(one(Rational{BigInt}))) == BigFloat
+
+    # BigFloat constructor respects global precision when not specified
+    let prec = precision(BigFloat) < 16 ? 256 : precision(BigFloat) ÷ 2
+        xs = Real[T(1) for T in (Int, BigInt, Float32, Float64, BigFloat)]
+        f = xs[end]
+        @test BigFloat(f) === f # no-op when precision of operand is the same as global's one
+        setprecision(prec) do
+            @test precision(xs[end]) != prec
+            for x in xs
+                @test precision(BigFloat(x)) == prec
+                @test precision(BigFloat(x, prec ÷ 2)) == prec ÷ 2
+            end
+        end
+    end
 end
 @testset "basic arithmetic" begin
     tol = 1e-12