diff --git a/clang/lib/CodeGen/CodeGenModule.cpp b/clang/lib/CodeGen/CodeGenModule.cpp
--- a/clang/lib/CodeGen/CodeGenModule.cpp
+++ b/clang/lib/CodeGen/CodeGenModule.cpp
@@ -3238,9 +3238,13 @@
     return ConstantAddress::invalid();
   }
 
-  auto *GV = new llvm::GlobalVariable(
-      getModule(), Init->getType(),
-      /*isConstant=*/true, llvm::GlobalValue::LinkOnceODRLinkage, Init, Name);
+  llvm::GlobalValue::LinkageTypes Linkage =
+      isExternallyVisible(TPO->getLinkageAndVisibility().getLinkage())
+          ? llvm::GlobalValue::LinkOnceODRLinkage
+          : llvm::GlobalValue::InternalLinkage;
+  auto *GV = new llvm::GlobalVariable(getModule(), Init->getType(),
+                                      /*isConstant=*/true, Linkage, Init, Name);
+  setGVProperties(GV, TPO);
   if (supportsCOMDAT())
     GV->setComdat(TheModule.getOrInsertComdat(GV->getName()));
   Emitter.finalize(GV);
diff --git a/clang/test/CodeGenCXX/template-param-objects-linkage.cpp b/clang/test/CodeGenCXX/template-param-objects-linkage.cpp
new file mode 100644
--- /dev/null
+++ b/clang/test/CodeGenCXX/template-param-objects-linkage.cpp
@@ -0,0 +1,26 @@
+// RUN: %clang_cc1 -triple x86_64-linux-gnu -std=c++20 %s -emit-llvm -o - | FileCheck %s
+
+struct S { char buf[32]; };
+template<S s> constexpr const char* f() { return s.buf; }
+const char* fbuf = f<S{"a"}>();
+// CHECK: @_ZTAXtl1StlA32_cLc97EEEE = linkonce_odr constant { <{ i8, [31 x i8] }> }
+
+namespace {
+  struct UN { char buf[64]; };
+}
+template <UN un> constexpr const char* g() { return un.buf; }
+const char* gbuf = g<UN{"b"}>();
+// CHECK: @_ZTAXtlN12_GLOBAL__N_12UNEtlA64_cLc98EEEE = internal constant { <{ i8, [63 x i8] }> }
+
+struct Foo { int *i; };
+int m = 0;
+namespace { int n; }
+
+template <Foo foo>
+const int* h() { return foo.i; }
+
+const int* hm = h<Foo{&m}>();
+// CHECK: @_ZTAXtl3FooadL_Z1mEEE = linkonce_odr constant %struct.Foo { ptr @m }
+
+const int* hn = h<Foo{&n}>();
+// CHECK: @_ZTAXtl3FooadL_ZN12_GLOBAL__N_11nEEEE = internal constant %struct.Foo { ptr @_ZN12_GLOBAL__N_11nE }
diff --git a/clang/test/CodeGenCXX/template-param-objects-visibility.cpp b/clang/test/CodeGenCXX/template-param-objects-visibility.cpp
new file mode 100644
--- /dev/null
+++ b/clang/test/CodeGenCXX/template-param-objects-visibility.cpp
@@ -0,0 +1,11 @@
+// RUN: %clang_cc1 -triple x86_64-linux-gnu -std=c++20 %s -emit-llvm -o - | FileCheck %s
+
+struct S { char buf[32]; };
+template<S s> constexpr const char* f() { return s.buf; }
+const char* fbuf = f<S{"a"}>();
+// CHECK: @_ZTAXtl1StlA32_cLc97EEEE = linkonce_odr constant { <{ i8, [31 x i8] }> }
+
+struct __attribute__ ((visibility ("hidden"))) HN { char buf[64]; };
+template <HN hn> constexpr const char* g() { return hn.buf; }
+const char* gbuf = g<HN{"b"}>();
+// CHECK: @_ZTAXtl2HNtlA64_cLc98EEEE = linkonce_odr hidden constant { <{ i8, [63 x i8] }> }
diff --git a/clang/test/CodeGenCXX/template-param-objects.cpp b/clang/test/CodeGenCXX/template-param-objects.cpp
--- a/clang/test/CodeGenCXX/template-param-objects.cpp
+++ b/clang/test/CodeGenCXX/template-param-objects.cpp
@@ -7,7 +7,9 @@
 
 // ITANIUM: [[HELLO:@_ZTAXtl1StlA32_cLc104ELc101ELc108ELc108ELc111ELc32ELc119ELc111ELc114ELc108ELc100EEEE]]
 // MSABI: [[HELLO:@"[?][?]__N2US@@3D0GI@@0GF@@0GM@@0GM@@0GP@@0CA@@0HH@@0GP@@0HC@@0GM@@0GE@@0A@@0A@@0A@@0A@@0A@@0A@@0A@@0A@@0A@@0A@@0A@@0A@@0A@@0A@@0A@@0A@@0A@@0A@@0A@@0A@@0A@@@@@"]]
-// CHECK-SAME: = linkonce_odr constant { <{ [11 x i8], [21 x i8] }> } { <{ [11 x i8], [21 x i8] }> <{ [11 x i8] c"hello world", [21 x i8] zeroinitializer }> }, comdat
+// ITANIUM-SAME: = linkonce_odr constant { <{ [11 x i8], [21 x i8] }> } { <{ [11 x i8], [21 x i8] }> <{ [11 x i8] c"hello world", [21 x i8] zeroinitializer }> }, comdat
+// MSABI-SAME: = linkonce_odr dso_local constant { <{ [11 x i8], [21 x i8] }> } { <{ [11 x i8], [21 x i8] }> <{ [11 x i8] c"hello world", [21 x i8] zeroinitializer }> }, comdat
+
 
 // ITANIUM: @p
 // MSABI: @"?p@@3PEBDEB"