diff --git a/mlir/include/mlir/Dialect/Bufferization/Transforms/BufferUtils.h b/mlir/include/mlir/Dialect/Bufferization/Transforms/BufferUtils.h
--- a/mlir/include/mlir/Dialect/Bufferization/Transforms/BufferUtils.h
+++ b/mlir/include/mlir/Dialect/Bufferization/Transforms/BufferUtils.h
@@ -125,7 +125,8 @@
 // Globals are created lazily at the top of the enclosing ModuleOp with pretty
 // names. Duplicates are avoided.
 FailureOr<memref::GlobalOp> getGlobalFor(arith::ConstantOp constantOp,
-                                         uint64_t alignment);
+                                         uint64_t alignment,
+                                         Attribute memorySpace);
 
 } // namespace bufferization
 } // namespace mlir
diff --git a/mlir/lib/Dialect/Arith/Transforms/BufferizableOpInterfaceImpl.cpp b/mlir/lib/Dialect/Arith/Transforms/BufferizableOpInterfaceImpl.cpp
--- a/mlir/lib/Dialect/Arith/Transforms/BufferizableOpInterfaceImpl.cpp
+++ b/mlir/lib/Dialect/Arith/Transforms/BufferizableOpInterfaceImpl.cpp
@@ -26,11 +26,6 @@
                           const BufferizationOptions &options) const {
     auto constantOp = cast<arith::ConstantOp>(op);
 
-    // TODO: Implement memory space for this op. E.g., by adding a memory_space
-    // attribute to ConstantOp.
-    if (options.defaultMemorySpace != Attribute())
-      return op->emitError("memory space not implemented yet");
-
     // Only ranked tensors are supported.
     if (!constantOp.getType().isa<RankedTensorType>())
       return failure();
@@ -42,8 +37,8 @@
 
     // Create global memory segment and replace tensor with memref pointing to
     // that memory segment.
-    FailureOr<memref::GlobalOp> globalOp =
-        getGlobalFor(constantOp, options.bufferAlignment);
+    FailureOr<memref::GlobalOp> globalOp = getGlobalFor(
+        constantOp, options.bufferAlignment, *options.defaultMemorySpace);
     if (failed(globalOp))
       return failure();
     memref::GlobalOp globalMemref = *globalOp;
diff --git a/mlir/lib/Dialect/Bufferization/Transforms/BufferUtils.cpp b/mlir/lib/Dialect/Bufferization/Transforms/BufferUtils.cpp
--- a/mlir/lib/Dialect/Bufferization/Transforms/BufferUtils.cpp
+++ b/mlir/lib/Dialect/Bufferization/Transforms/BufferUtils.cpp
@@ -147,7 +147,8 @@
 //===----------------------------------------------------------------------===//
 
 FailureOr<memref::GlobalOp>
-bufferization::getGlobalFor(arith::ConstantOp constantOp, uint64_t alignment) {
+bufferization::getGlobalFor(arith::ConstantOp constantOp, uint64_t alignment,
+                            Attribute memorySpace) {
   auto type = constantOp.getType().cast<RankedTensorType>();
   auto moduleOp = constantOp->getParentOfType<ModuleOp>();
   if (!moduleOp)
@@ -184,10 +185,12 @@
                     : IntegerAttr();
 
   BufferizeTypeConverter typeConverter;
+  auto memrefType = typeConverter.convertType(type).cast<MemRefType>();
+  memrefType = MemRefType::Builder(memrefType).setMemorySpace(memorySpace);
   auto global = globalBuilder.create<memref::GlobalOp>(
       constantOp.getLoc(), (Twine("__constant_") + os.str()).str(),
       /*sym_visibility=*/globalBuilder.getStringAttr("private"),
-      /*type=*/typeConverter.convertType(type).cast<MemRefType>(),
+      /*type=*/memrefType,
       /*initial_value=*/constantOp.getValue().cast<ElementsAttr>(),
       /*constant=*/true,
       /*alignment=*/memrefAlignment);
diff --git a/mlir/test/Dialect/Arith/one-shot-bufferize-memory-space-invalid.mlir b/mlir/test/Dialect/Arith/one-shot-bufferize-memory-space-invalid.mlir
--- a/mlir/test/Dialect/Arith/one-shot-bufferize-memory-space-invalid.mlir
+++ b/mlir/test/Dialect/Arith/one-shot-bufferize-memory-space-invalid.mlir
@@ -10,13 +10,3 @@
   %r = arith.select %c, %0, %1 : tensor<10xf32>
   func.return %r : tensor<10xf32>
 }
-
-// -----
-
-func.func @constant_memory_space(%idx: index, %v: i32) -> tensor<3xi32> {
-  // expected-error @+2 {{memory space not implemented yet}}
-  // expected-error @+1 {{failed to bufferize op}}
-  %cst = arith.constant dense<[5, 1000, 20]> : tensor<3xi32>
-  %0 = tensor.insert %v into %cst[%idx] : tensor<3xi32>
-  return %0 : tensor<3xi32>
-}
\ No newline at end of file
diff --git a/mlir/test/Dialect/Arith/one-shot-bufferize-memory-space.mlir b/mlir/test/Dialect/Arith/one-shot-bufferize-memory-space.mlir
new file mode 100644
--- /dev/null
+++ b/mlir/test/Dialect/Arith/one-shot-bufferize-memory-space.mlir
@@ -0,0 +1,10 @@
+// RUN: mlir-opt %s -one-shot-bufferize="must-infer-memory-space" | FileCheck %s
+
+// CHECK-LABEL:   memref.global "private" constant @__constant_3xi32 : memref<3xi32> = dense<[5, 1000, 20]> {alignment = 64 : i64}
+// CHECK-LABEL:   func.func @constant_memory_space(
+// CHECK:           %[[VAL_2:.*]] = memref.get_global @__constant_3xi32 : memref<3xi32>
+func.func @constant_memory_space(%idx: index, %v: i32) -> tensor<3xi32> {
+  %cst = arith.constant dense<[5, 1000, 20]> : tensor<3xi32>
+  %0 = tensor.insert %v into %cst[%idx] : tensor<3xi32>
+  return %0 : tensor<3xi32>
+}
\ No newline at end of file