diff --git a/mlir/include/mlir/Dialect/SparseTensor/IR/SparseTensorAttrDefs.td b/mlir/include/mlir/Dialect/SparseTensor/IR/SparseTensorAttrDefs.td
index afd978c1c57ebd..38c7200afb41ff 100644
--- a/mlir/include/mlir/Dialect/SparseTensor/IR/SparseTensorAttrDefs.td
+++ b/mlir/include/mlir/Dialect/SparseTensor/IR/SparseTensorAttrDefs.td
@@ -134,7 +134,7 @@ def SparseTensorEncodingAttr : SparseTensor_Attr<"SparseTensorEncoding",
     level-coordinates. The dimension-expressions collectively define the inverse map,
     which only needs to be provided for elaborate cases where it cannot be inferred
     automatically.
-    
+
     Each dimension could also have an optional `SparseTensorDimSliceAttr`.
     Within the sparse storage format, we refer to indices that are stored explicitly
     as **coordinates** and offsets into the storage format as **positions**.
@@ -237,10 +237,10 @@ def SparseTensorEncodingAttr : SparseTensor_Attr<"SparseTensorEncoding",
     }>
     ... tensor<20x30xf32, #BSR_explicit> ...
 
-    // ELL format. 
+    // ELL format.
     // In the simple format for matrix, one array stores values and another
     // array stores column indices. The arrays have the same number of rows
-    // as the original matrix, but only have as many columns as 
+    // as the original matrix, but only have as many columns as
     // the maximum number of nonzeros on a row of the original matrix.
     // There are many variants for ELL such as jagged diagonal scheme.
     // To implement ELL, map provides a notion of "counting a
@@ -376,6 +376,9 @@ def SparseTensorEncodingAttr : SparseTensor_Attr<"SparseTensorEncoding",
     /// the null encoding (since dense-tensors are always all-dense).
     bool isAllDense() const;
 
+    /// Returns true if it is a sparse tensor encoding in COO format.
+    bool isCOO() const;
+
     /// Returns true if every level is ordered.  Also returns true for
     /// the null encoding (since dense-tensors are always all-ordered).
     bool isAllOrdered() const;
@@ -468,6 +471,10 @@ def SparseTensorStorageSpecifierKindAttr
 def IsSparseTensorPred
   : CPred<"!!::mlir::sparse_tensor::getSparseTensorEncoding($_self)">;
 
+def IsCOOPred
+  : CPred<"!!::mlir::sparse_tensor::getSparseTensorEncoding($_self) && "
+          "  ::mlir::sparse_tensor::getSparseTensorEncoding($_self).isCOO()">;
+
 def IsSparseTensorSlicePred
   : CPred<"!!::mlir::sparse_tensor::getSparseTensorEncoding($_self) && "
           "  ::mlir::sparse_tensor::getSparseTensorEncoding($_self).isSlice()">;
@@ -478,10 +485,14 @@ def IsSparseTensorSlicePred
 class SparseTensorOf<list<Type> allowedTypes>
   : TensorOf<allowedTypes, [IsSparseTensorPred], "sparse tensor">;
 
+class COOSparseTensorOf<list<Type> allowedTypes>
+  : TensorOf<allowedTypes, [IsCOOPred], "COO sparse tensor">;
+
 class SparseTensorSliceOf<list<Type> allowedTypes>
   : TensorOf<allowedTypes, [IsSparseTensorSlicePred], "sparse tensor slice">;
 
 def AnySparseTensor : SparseTensorOf<[AnyType]>;
+def AnyCOOSparseTensor : COOSparseTensorOf<[AnyType]>;
 def AnySparseTensorSlice : SparseTensorSliceOf<[AnyType]>;
 
 class RankedSparseTensorOf<list<Type> allowedTypes>
diff --git a/mlir/include/mlir/Dialect/SparseTensor/IR/SparseTensorOps.td b/mlir/include/mlir/Dialect/SparseTensor/IR/SparseTensorOps.td
index 042ae9693f486e..afbabb97eb71fc 100644
--- a/mlir/include/mlir/Dialect/SparseTensor/IR/SparseTensorOps.td
+++ b/mlir/include/mlir/Dialect/SparseTensor/IR/SparseTensorOps.td
@@ -770,7 +770,7 @@ def SparseTensor_OutOp : SparseTensor_Op<"out", []>,
 }
 
 //===----------------------------------------------------------------------===//
-// Sparse Tensor Sorting Operations.
+// Sparse Tensor Sorting/Ordering Operations.
 //===----------------------------------------------------------------------===//
 
 def SparseTensor_SortOp : SparseTensor_Op<"sort">,
@@ -809,6 +809,36 @@ def SparseTensor_SortOp : SparseTensor_Op<"sort">,
   let hasVerifier = 1;
 }
 
+def SparseTensor_ReorderCOOOp : SparseTensor_Op<"reorder_coo", [Pure]>,
+    Arguments<(ins AnyCOOSparseTensor: $input_coo,
+                   SparseTensorSortKindAttr:$algorithm)>,
+    Results<(outs AnyCOOSparseTensor: $result_coo)> {
+  let summary = "Reorder the input COO such that it has the the same order as "
+                "the output COO";
+  let description = [{
+    sparse_tensor.reorder_coo reorder input COO to the same order as specified by
+    the output format. E.g., reorder an unordered COO into an ordered one.
+
+    The input and result COO tensor must have the same element type, position type and
+    coordinate type. At the moment, the operation also only supports ordering
+    input and result COO with the same dim2lvl map.
+
+    Example:
+
+    ```mlir
+    %res = sparse_tensor.reorder_coo quick_sort %coo : tensor<?x?xf64 : #Unordered_COO> to
+                                                       tensor<?x?xf64 : #Ordered_COO>
+
+    ```
+  }];
+
+  let assemblyFormat = "$algorithm $input_coo attr-dict"
+                       "`:` type($input_coo) `to` type($result_coo)";
+
+  let hasFolder = 1;
+  let hasVerifier = 1;
+}
+
 //===----------------------------------------------------------------------===//
 // Sparse Tensor Syntax Operations.
 //===----------------------------------------------------------------------===//
diff --git a/mlir/lib/Dialect/SparseTensor/IR/SparseTensorDialect.cpp b/mlir/lib/Dialect/SparseTensor/IR/SparseTensorDialect.cpp
index 5b84d2158bc828..ef9d4fea68628b 100644
--- a/mlir/lib/Dialect/SparseTensor/IR/SparseTensorDialect.cpp
+++ b/mlir/lib/Dialect/SparseTensor/IR/SparseTensorDialect.cpp
@@ -336,6 +336,10 @@ bool SparseTensorEncodingAttr::isAllDense() const {
   return !getImpl() || llvm::all_of(getLvlTypes(), isDenseDLT);
 }
 
+bool SparseTensorEncodingAttr::isCOO() const {
+  return getImpl() && isCOOType(*this, 0, true);
+}
+
 bool SparseTensorEncodingAttr::isAllOrdered() const {
   return !getImpl() || llvm::all_of(getLvlTypes(), isOrderedDLT);
 }
@@ -1417,6 +1421,29 @@ LogicalResult ForeachOp::verify() {
   return success();
 }
 
+OpFoldResult ReorderCOOOp::fold(FoldAdaptor adaptor) {
+  if (getSparseTensorEncoding(getInputCoo().getType()) ==
+      getSparseTensorEncoding(getResultCoo().getType()))
+    return getInputCoo();
+
+  return {};
+}
+
+LogicalResult ReorderCOOOp::verify() {
+  SparseTensorType srcStt = getSparseTensorType(getInputCoo());
+  SparseTensorType dstStt = getSparseTensorType(getResultCoo());
+
+  if (!srcStt.hasSameDimToLvl(dstStt))
+    emitError("Unmatched dim2lvl map between input and result COO");
+
+  if (srcStt.getPosType() != dstStt.getPosType() ||
+      srcStt.getCrdType() != dstStt.getCrdType() ||
+      srcStt.getElementType() != dstStt.getElementType()) {
+    emitError("Unmatched storage format between input and result COO");
+  }
+  return success();
+}
+
 LogicalResult ReduceOp::verify() {
   Type inputType = getX().getType();
   // Check correct number of block arguments and return type.
diff --git a/mlir/test/Dialect/SparseTensor/fold.mlir b/mlir/test/Dialect/SparseTensor/fold.mlir
index 089431f9e18e90..3dd1a629c129ff 100644
--- a/mlir/test/Dialect/SparseTensor/fold.mlir
+++ b/mlir/test/Dialect/SparseTensor/fold.mlir
@@ -62,3 +62,16 @@ func.func @sparse_get_specifier_dce_fold(%arg0: !sparse_tensor.storage_specifier
        : !sparse_tensor.storage_specifier<#SparseVector>
   return %2 : index
 }
+
+
+
+#COO = #sparse_tensor.encoding<{map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton)}>
+
+// CHECK-LABEL: func @sparse_reorder_coo(
+//  CHECK-SAME: %[[A:.*]]: tensor<?x?xf32, #sparse_tensor.encoding<{{{.*}}}>>
+//   CHECK-NOT: %[[R:.*]] = sparse_tensor.reorder_coo
+//       CHECK: return %[[A]]
+func.func @sparse_reorder_coo(%arg0 : tensor<?x?xf32, #COO>) -> tensor<?x?xf32, #COO> {
+  %ret = sparse_tensor.reorder_coo quick_sort %arg0 : tensor<?x?xf32, #COO> to tensor<?x?xf32, #COO>
+  return %ret : tensor<?x?xf32, #COO>
+}
diff --git a/mlir/test/Dialect/SparseTensor/invalid.mlir b/mlir/test/Dialect/SparseTensor/invalid.mlir
index 2df4237efa0bbe..805f3d161921c1 100644
--- a/mlir/test/Dialect/SparseTensor/invalid.mlir
+++ b/mlir/test/Dialect/SparseTensor/invalid.mlir
@@ -839,3 +839,25 @@ func.func @sparse_alloc_escapes(%arg0: index) -> tensor<10x?xf64, #CSR> {
   %0 = bufferization.alloc_tensor(%arg0) : tensor<10x?xf64, #CSR>
   return %0: tensor<10x?xf64, #CSR>
 }
+
+// -----
+
+#UnorderedCOO = #sparse_tensor.encoding<{map = (d0, d1) -> (d0 : compressed(nonunique, nonordered), d1 : singleton(nonordered))}>
+#OrderedCOOPerm = #sparse_tensor.encoding<{map = (d0, d1) -> (d1 : compressed(nonunique), d0 : singleton)}>
+
+func.func @sparse_permuted_reorder_coo(%arg0 : tensor<?x?xf32, #UnorderedCOO>) -> tensor<?x?xf32, #OrderedCOOPerm> {
+  // expected-error@+1 {{Unmatched dim2lvl map between input and result COO}}
+  %ret = sparse_tensor.reorder_coo quick_sort %arg0 : tensor<?x?xf32, #UnorderedCOO> to tensor<?x?xf32, #OrderedCOOPerm>
+  return %ret : tensor<?x?xf32, #OrderedCOOPerm>
+}
+
+// -----
+
+#UnorderedCOO = #sparse_tensor.encoding<{map = (d0, d1) -> (d0 : compressed(nonunique, nonordered), d1 : singleton(nonordered))}>
+#OrderedCOO = #sparse_tensor.encoding<{map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton)}>
+
+func.func @sparse_permuted_reorder_coo(%arg0 : tensor<?x?xf32, #UnorderedCOO>) -> tensor<?x?xf64, #OrderedCOO> {
+  // expected-error@+1 {{Unmatched storage format between input and result COO}}
+  %ret = sparse_tensor.reorder_coo quick_sort %arg0 : tensor<?x?xf32, #UnorderedCOO> to tensor<?x?xf64, #OrderedCOO>
+  return %ret : tensor<?x?xf64, #OrderedCOO>
+}
diff --git a/mlir/test/Dialect/SparseTensor/roundtrip.mlir b/mlir/test/Dialect/SparseTensor/roundtrip.mlir
index 82267be34b9384..cbc3bb824924cd 100644
--- a/mlir/test/Dialect/SparseTensor/roundtrip.mlir
+++ b/mlir/test/Dialect/SparseTensor/roundtrip.mlir
@@ -633,3 +633,17 @@ func.func @sparse_sort_coo_stable(%arg0: index, %arg1: memref<?xi64>, %arg2: mem
   sparse_tensor.sort insertion_sort_stable %arg0, %arg1 jointly %arg2 {perm_map = #ID_MAP, ny = 1 : index}: memref<?xi64> jointly memref<?xf32>
   return %arg1, %arg2 : memref<?xi64>, memref<?xf32>
 }
+
+// -----
+
+#UnorderedCOO = #sparse_tensor.encoding<{map = (d0, d1) -> (d0 : compressed(nonunique, nonordered), d1 : singleton(nonordered))}>
+#OrderedCOO = #sparse_tensor.encoding<{map = (d0, d1) -> (d0 : compressed(nonunique), d1 : singleton)}>
+
+// CHECK-LABEL: func @sparse_reorder_coo(
+//  CHECK-SAME: %[[A:.*]]: tensor<?x?xf32, #sparse_tensor.encoding<{{{.*}}}>>
+//       CHECK: %[[R:.*]] = sparse_tensor.reorder_coo quick_sort %[[A]]
+//       CHECK: return %[[R]]
+func.func @sparse_reorder_coo(%arg0 : tensor<?x?xf32, #UnorderedCOO>) -> tensor<?x?xf32, #OrderedCOO> {
+  %ret = sparse_tensor.reorder_coo quick_sort %arg0 : tensor<?x?xf32, #UnorderedCOO> to tensor<?x?xf32, #OrderedCOO>
+  return %ret : tensor<?x?xf32, #OrderedCOO>
+}