diff --git a/mlir/include/mlir-c/Dialect/LLVM.h b/mlir/include/mlir-c/Dialect/LLVM.h
index 0e6434073437a..ed9b23c343150 100644
--- a/mlir/include/mlir-c/Dialect/LLVM.h
+++ b/mlir/include/mlir-c/Dialect/LLVM.h
@@ -175,17 +175,17 @@ MLIR_CAPI_EXPORTED MlirAttribute mlirLLVMComdatAttrGet(MlirContext ctx,
                                                        MlirLLVMComdat comdat);
 
 enum MlirLLVMLinkage {
-  MlirLLVMLinkagePrivate = 0,
-  MlirLLVMLinkageInternal = 1,
-  MlirLLVMLinkageAvailableExternally = 2,
-  MlirLLVMLinkageLinkonce = 3,
+  MlirLLVMLinkageExternal = 0,
+  MlirLLVMLinkageAvailableExternally = 1,
+  MlirLLVMLinkageLinkonce = 2,
+  MlirLLVMLinkageLinkonceODR = 3,
   MlirLLVMLinkageWeak = 4,
-  MlirLLVMLinkageCommon = 5,
+  MlirLLVMLinkageWeakODR = 5,
   MlirLLVMLinkageAppending = 6,
-  MlirLLVMLinkageExternWeak = 7,
-  MlirLLVMLinkageLinkonceODR = 8,
-  MlirLLVMLinkageWeakODR = 9,
-  MlirLLVMLinkageExternal = 10,
+  MlirLLVMLinkageInternal = 7,
+  MlirLLVMLinkagePrivate = 8,
+  MlirLLVMLinkageExternWeak = 9,
+  MlirLLVMLinkageCommon = 10,
 };
 typedef enum MlirLLVMLinkage MlirLLVMLinkage;
 
diff --git a/mlir/include/mlir/Dialect/LLVMIR/LLVMEnums.td b/mlir/include/mlir/Dialect/LLVMIR/LLVMEnums.td
index 4a43c16903394..c08b75de03647 100644
--- a/mlir/include/mlir/Dialect/LLVMIR/LLVMEnums.td
+++ b/mlir/include/mlir/Dialect/LLVMIR/LLVMEnums.td
@@ -615,40 +615,40 @@ def ICmpPredicate : LLVM_EnumAttr<
 //===----------------------------------------------------------------------===//
 
 // Linkage attribute is used on functions and globals. The order follows that of
-// https://llvm.org/docs/LangRef.html#linkage-types. The names are equivalent to
-// visible names in the IR rather than to enum values names in llvm::GlobalValue
-// since the latter is easier to change.
-def LinkagePrivate
-    : LLVM_EnumAttrCase<"Private", "private", "PrivateLinkage", 0>;
-def LinkageInternal
-    : LLVM_EnumAttrCase<"Internal", "internal", "InternalLinkage", 1>;
+// llvm::GlobalValue::LinkageTypes from llvm/IR/GlobalValue.h. The names are
+// equivalent to visible names in the IR rather than to enum values names in
+// llvm::GlobalValue since the latter is easier to change.
+def LinkageExternal
+    : LLVM_EnumAttrCase<"External", "external", "ExternalLinkage", 0>;
 def LinkageAvailableExternally
     : LLVM_EnumAttrCase<"AvailableExternally", "available_externally",
-                        "AvailableExternallyLinkage", 2>;
+                        "AvailableExternallyLinkage", 1>;
 def LinkageLinkonce
-    : LLVM_EnumAttrCase<"Linkonce", "linkonce", "LinkOnceAnyLinkage", 3>;
+    : LLVM_EnumAttrCase<"Linkonce", "linkonce", "LinkOnceAnyLinkage", 2>;
+def LinkageLinkonceODR
+    : LLVM_EnumAttrCase<"LinkonceODR", "linkonce_odr", "LinkOnceODRLinkage", 3>;
 def LinkageWeak
     : LLVM_EnumAttrCase<"Weak", "weak", "WeakAnyLinkage", 4>;
-def LinkageCommon
-    : LLVM_EnumAttrCase<"Common", "common", "CommonLinkage", 5>;
+def LinkageWeakODR
+    : LLVM_EnumAttrCase<"WeakODR", "weak_odr", "WeakODRLinkage", 5>;
 def LinkageAppending
     : LLVM_EnumAttrCase<"Appending", "appending", "AppendingLinkage", 6>;
+def LinkageInternal
+    : LLVM_EnumAttrCase<"Internal", "internal", "InternalLinkage", 7>;
+def LinkagePrivate
+    : LLVM_EnumAttrCase<"Private", "private", "PrivateLinkage", 8>;
 def LinkageExternWeak
-   : LLVM_EnumAttrCase<"ExternWeak", "extern_weak", "ExternalWeakLinkage", 7>;
-def LinkageLinkonceODR
-    : LLVM_EnumAttrCase<"LinkonceODR", "linkonce_odr", "LinkOnceODRLinkage", 8>;
-def LinkageWeakODR
-    : LLVM_EnumAttrCase<"WeakODR", "weak_odr", "WeakODRLinkage", 9>;
-def LinkageExternal
-    : LLVM_EnumAttrCase<"External", "external", "ExternalLinkage", 10>;
+   : LLVM_EnumAttrCase<"ExternWeak", "extern_weak", "ExternalWeakLinkage", 9>;
+def LinkageCommon
+    : LLVM_EnumAttrCase<"Common", "common", "CommonLinkage", 10>;
 
 def LinkageEnum : LLVM_EnumAttr<
     "Linkage",
     "::llvm::GlobalValue::LinkageTypes",
     "LLVM linkage types",
-    [LinkagePrivate, LinkageInternal, LinkageAvailableExternally,
-     LinkageLinkonce, LinkageWeak, LinkageCommon, LinkageAppending,
-     LinkageExternWeak, LinkageLinkonceODR, LinkageWeakODR, LinkageExternal]> {
+    [LinkageExternal, LinkageAvailableExternally, LinkageLinkonce,
+      LinkageLinkonceODR, LinkageWeak, LinkageWeakODR, LinkageAppending,
+      LinkageInternal, LinkagePrivate, LinkageExternWeak, LinkageCommon]> {
   let cppNamespace = "::mlir::LLVM::linkage";
 }