Index: lib/Format/TokenAnnotator.cpp
===================================================================
--- lib/Format/TokenAnnotator.cpp
+++ lib/Format/TokenAnnotator.cpp
@@ -2249,6 +2249,9 @@
       return 500;
   }
 
+  if (Left.is(tok::coloncolon) ||
+      (Right.is(tok::period) && Style.Language == FormatStyle::LK_Proto))
+    return 500;
   if (Right.isOneOf(TT_StartOfName, TT_FunctionDeclarationName) ||
       Right.is(tok::kw_operator)) {
     if (Line.startsWith(tok::kw_for) && Right.PartOfMultiVariableDeclStmt)
@@ -2267,9 +2270,6 @@
     return 160;
   if (Left.is(TT_CastRParen))
     return 100;
-  if (Left.is(tok::coloncolon) ||
-      (Right.is(tok::period) && Style.Language == FormatStyle::LK_Proto))
-    return 500;
   if (Left.isOneOf(tok::kw_class, tok::kw_struct))
     return 5000;
   if (Left.is(tok::comment))
Index: unittests/Format/FormatTest.cpp
===================================================================
--- unittests/Format/FormatTest.cpp
+++ unittests/Format/FormatTest.cpp
@@ -4183,6 +4183,18 @@
                Style);
 }
 
+TEST_F(FormatTest, DontBreakBeforeQualifiedOperator) {
+  // Regression test for https://bugs.llvm.org/show_bug.cgi?id=40516:
+  // Prefer keeping `::` followed by `operator` together.
+  EXPECT_EQ("const aaaa::bbbbbbb &\n"
+            "ccccccccc::operator++() {\n"
+            "  stuff();\n"
+            "}",
+            format("const aaaa::bbbbbbb\n"
+                   "&ccccccccc::operator++() { stuff(); }",
+                   getLLVMStyleWithColumns(40)));
+}
+
 TEST_F(FormatTest, TrailingReturnType) {
   verifyFormat("auto foo() -> int;\n");
   verifyFormat("struct S {\n"