diff --git a/clang-tools-extra/clang-tidy/misc/UseAnonymousNamespaceCheck.h b/clang-tools-extra/clang-tidy/misc/UseAnonymousNamespaceCheck.h
--- a/clang-tools-extra/clang-tidy/misc/UseAnonymousNamespaceCheck.h
+++ b/clang-tools-extra/clang-tidy/misc/UseAnonymousNamespaceCheck.h
@@ -10,6 +10,7 @@
 #define LLVM_CLANG_TOOLS_EXTRA_CLANG_TIDY_MISC_USEANONYMOUSNAMESPACECHECK_H
 
 #include "../ClangTidyCheck.h"
+#include "../utils/FileExtensionsUtils.h"
 
 namespace clang {
 namespace tidy {
@@ -23,8 +24,7 @@
 /// http://clang.llvm.org/extra/clang-tidy/checks/modernize/use-anonymous-namespace.html
 class UseAnonymousNamespaceCheck : public ClangTidyCheck {
 public:
-  UseAnonymousNamespaceCheck(StringRef Name, ClangTidyContext *Context)
-      : ClangTidyCheck(Name, Context) {}
+  UseAnonymousNamespaceCheck(StringRef Name, ClangTidyContext *Context);
   bool isLanguageVersionSupported(const LangOptions &LangOpts) const override {
     return LangOpts.CPlusPlus;
   }
@@ -32,6 +32,7 @@
   void check(const ast_matchers::MatchFinder::MatchResult &Result) override;
 
 private:
+  utils::FileExtensionsSet HeaderFileExtensions;
   template <typename T> void processMatch(const T *MatchedDecl);
 };
 
diff --git a/clang-tools-extra/clang-tidy/misc/UseAnonymousNamespaceCheck.cpp b/clang-tools-extra/clang-tidy/misc/UseAnonymousNamespaceCheck.cpp
--- a/clang-tools-extra/clang-tidy/misc/UseAnonymousNamespaceCheck.cpp
+++ b/clang-tools-extra/clang-tidy/misc/UseAnonymousNamespaceCheck.cpp
@@ -37,16 +37,32 @@
   return false;
 }
 
+UseAnonymousNamespaceCheck::UseAnonymousNamespaceCheck(
+    StringRef Name, ClangTidyContext *Context)
+    : ClangTidyCheck(Name, Context) {
+  if (!utils::parseFileExtensions(utils::defaultHeaderFileExtensions(),
+                                  HeaderFileExtensions,
+                                  utils::defaultFileExtensionDelimiters())) {
+    this->configurationDiag("Invalid header file extension: '%0'")
+        << utils::defaultHeaderFileExtensions();
+  }
+}
+
 template <typename T>
 void UseAnonymousNamespaceCheck::processMatch(const T *MatchedDecl) {
+  // Enforce anonymous namespaces only in source files, not headers
+  SourceLocation Loc = MatchedDecl->getLocation();
+  SourceManager &SM = MatchedDecl->getASTContext().getSourceManager();
+  if (utils::isSpellingLocInHeaderFile(Loc, SM, HeaderFileExtensions))
+    return;
+
   StringRef Type = llvm::isa<VarDecl>(MatchedDecl) ? "variable" : "function";
   if (isInAnonymousNamespace(MatchedDecl))
-    diag(MatchedDecl->getLocation(), "%0 %1 declared 'static' in "
-                                     "anonymous namespace, remove 'static'")
+    diag(Loc, "%0 %1 declared 'static' in "
+              "anonymous namespace, remove 'static'")
         << Type << MatchedDecl;
   else
-    diag(MatchedDecl->getLocation(),
-         "%0 %1 declared 'static', move to anonymous namespace instead")
+    diag(Loc, "%0 %1 declared 'static', move to anonymous namespace instead")
         << Type << MatchedDecl;
 }
 
@@ -54,7 +70,8 @@
   Finder->addMatcher(
       functionDecl(isStatic(), unless(isMemberFunction())).bind("func"), this);
   Finder->addMatcher(
-      varDecl(isStatic(), unless(anyOf(isStaticLocal(), isStaticDataMember())))
+      varDecl(isStatic(), unless(anyOf(isStaticLocal(), isStaticDataMember(),
+                                       hasType(isConstQualified()))))
           .bind("var"),
       this);
 }
diff --git a/clang-tools-extra/test/clang-tidy/checkers/misc/Inputs/use-anonymous-namespace.h b/clang-tools-extra/test/clang-tidy/checkers/misc/Inputs/use-anonymous-namespace.h
new file mode 100644
--- /dev/null
+++ b/clang-tools-extra/test/clang-tidy/checkers/misc/Inputs/use-anonymous-namespace.h
@@ -0,0 +1,3 @@
+// Should not warn here, do not require anonymous namespaces in headers
+static int gv{123};
+static void gf(){}
diff --git a/clang-tools-extra/test/clang-tidy/checkers/misc/use-anonymous-namespace.cpp b/clang-tools-extra/test/clang-tidy/checkers/misc/use-anonymous-namespace.cpp
--- a/clang-tools-extra/test/clang-tidy/checkers/misc/use-anonymous-namespace.cpp
+++ b/clang-tools-extra/test/clang-tidy/checkers/misc/use-anonymous-namespace.cpp
@@ -1,4 +1,5 @@
-// RUN: %check_clang_tidy %s misc-use-anonymous-namespace %t
+// RUN: %check_clang_tidy %s misc-use-anonymous-namespace %t -- -header-filter=.* -- -I%S/Inputs
+#include "use-anonymous-namespace.h"
 
 static void f1();
 // CHECK-MESSAGES: :[[@LINE-1]]:13: warning: function 'f1' declared 'static', move to anonymous namespace instead [misc-use-anonymous-namespace]
@@ -57,3 +58,7 @@
 {
   static int x;
 }
+
+// OK
+static const int v8{123};
+static constexpr int v9{123};