diff --git a/clang/lib/Format/TokenAnnotator.cpp b/clang/lib/Format/TokenAnnotator.cpp
--- a/clang/lib/Format/TokenAnnotator.cpp
+++ b/clang/lib/Format/TokenAnnotator.cpp
@@ -2089,6 +2089,10 @@
       return TT_UnaryOperator;
 
     const FormatToken *NextToken = Tok.getNextNonComment();
+
+    if (InTemplateArgument && NextToken && NextToken->is(tok::kw_noexcept))
+      return TT_BinaryOperator;
+
     if (!NextToken ||
         NextToken->isOneOf(tok::arrow, tok::equal, tok::kw_noexcept) ||
         NextToken->canBePointerOrReferenceQualifier() ||
diff --git a/clang/unittests/Format/FormatTest.cpp b/clang/unittests/Format/FormatTest.cpp
--- a/clang/unittests/Format/FormatTest.cpp
+++ b/clang/unittests/Format/FormatTest.cpp
@@ -9512,6 +9512,8 @@
   verifyFormat("f(aaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\n"
                "      .template operator()<A>());",
                getLLVMStyleWithColumns(35));
+  verifyFormat("bool_constant<a && noexcept(f())>");
+  verifyFormat("bool_constant<a || noexcept(f())>");
 
   // Not template parameters.
   verifyFormat("return a < b && c > d;");