diff --git a/clang-tools-extra/clang-tidy/misc/DefinitionsInHeadersCheck.cpp b/clang-tools-extra/clang-tidy/misc/DefinitionsInHeadersCheck.cpp
--- a/clang-tools-extra/clang-tidy/misc/DefinitionsInHeadersCheck.cpp
+++ b/clang-tools-extra/clang-tidy/misc/DefinitionsInHeadersCheck.cpp
@@ -134,6 +134,9 @@
          DiagnosticIDs::Note)
         << FixItHint::CreateInsertion(FD->getInnerLocStart(), "inline ");
   } else if (const auto *VD = dyn_cast<VarDecl>(ND)) {
+    // C++14 variable templates are allowed.
+    if (VD->getDescribedVarTemplate())
+      return;
     // Static data members of a class template are allowed.
     if (VD->getDeclContext()->isDependentContext() && VD->isStaticDataMember())
       return;
diff --git a/clang-tools-extra/docs/clang-tidy/checks/misc-definitions-in-headers.rst b/clang-tools-extra/docs/clang-tidy/checks/misc-definitions-in-headers.rst
--- a/clang-tools-extra/docs/clang-tidy/checks/misc-definitions-in-headers.rst
+++ b/clang-tools-extra/docs/clang-tidy/checks/misc-definitions-in-headers.rst
@@ -83,6 +83,10 @@
 
    constexpr int f10() { return 0; } // OK: constexpr function implies inline.
 
+   // OK: C++14 variable templates are inline.
+   template <class T>
+   constexpr T pi = T(3.1415926L);
+
 Options
 -------
 
diff --git a/clang-tools-extra/test/clang-tidy/checkers/misc-definitions-in-headers-1z.hpp b/clang-tools-extra/test/clang-tidy/checkers/misc-definitions-in-headers-1z.hpp
--- a/clang-tools-extra/test/clang-tidy/checkers/misc-definitions-in-headers-1z.hpp
+++ b/clang-tools-extra/test/clang-tidy/checkers/misc-definitions-in-headers-1z.hpp
@@ -1,4 +1,4 @@
-// RUN: %check_clang_tidy %s misc-definitions-in-headers %t -- -- -std=c++1z
+// RUN: %check_clang_tidy -std=c++17-or-later %s misc-definitions-in-headers %t
 
 class CE {
   constexpr static int i = 5; // OK: inline variable definition.
@@ -8,3 +8,7 @@
 
 int b = 1;
 // CHECK-MESSAGES: :[[@LINE-1]]:5: warning: variable 'b' defined in a header file; variable definitions in header files can lead to ODR violations [misc-definitions-in-headers]
+
+// OK: C++14 variable template.
+template <class T>
+constexpr T pi = T(3.1415926L);