diff --git a/mlir/lib/Dialect/Linalg/IR/LinalgInterfaces.cpp b/mlir/lib/Dialect/Linalg/IR/LinalgInterfaces.cpp
--- a/mlir/lib/Dialect/Linalg/IR/LinalgInterfaces.cpp
+++ b/mlir/lib/Dialect/Linalg/IR/LinalgInterfaces.cpp
@@ -338,10 +338,12 @@
     return op->emitOpError("expected at least one output operand");
   if (failed(OpTrait::impl::verifyNOperands(op, numInputs + numOutputs)))
     return failure();
-  // Should have at least one output tensor per result tensor.
-  // Can also have outbut buffers that do not correspond to results.
-  if (op->getNumResults() > linalgOp.getOutputTensorOperands().size())
-    return op->emitOpError("unexpected #results > #outputs");
+  // Verify the number of results matches the number of output tensors.
+  if (op->getNumResults() != linalgOp.getOutputTensorOperands().size())
+    return op->emitOpError("expected the number of results (")
+           << op->getNumResults()
+           << ") to be equal to the number of output tensors ("
+           << linalgOp.getOutputTensorOperands().size() << ")";
 
   // Before checking indexing maps, we need to make sure the attributes
   // referenced by it are valid.
@@ -394,10 +396,6 @@
         "all have buffer type");
 
   for (OpOperand *opOperand : linalgOp.getOutputTensorOperands()) {
-    // TODO: Enforce one output tensor per result?
-    if (opOperand->getOperandNumber() - linalgOp.getNumInputs() >=
-        linalgOp->getNumResults())
-      continue;
     OpResult result = linalgOp.getTiedOpResult(opOperand);
     if (result.getType() != opOperand->get().getType())
       return op->emitOpError("expected type of operand #")
diff --git a/mlir/lib/Dialect/Linalg/IR/LinalgOps.cpp b/mlir/lib/Dialect/Linalg/IR/LinalgOps.cpp
--- a/mlir/lib/Dialect/Linalg/IR/LinalgOps.cpp
+++ b/mlir/lib/Dialect/Linalg/IR/LinalgOps.cpp
@@ -458,10 +458,6 @@
   Type fillType = op.value().getType();
   if (getElementTypeOrSelf(output->get()) != fillType)
     return op.emitOpError("expects fill type to match view elemental type");
-  if (!op.getNumResults() && !output->get().getType().isa<MemRefType>()) {
-    return op.emitOpError(
-        "expected fill op with no result value to use memref type");
-  }
   return success();
 }
 
diff --git a/mlir/test/Dialect/Linalg/invalid.mlir b/mlir/test/Dialect/Linalg/invalid.mlir
--- a/mlir/test/Dialect/Linalg/invalid.mlir
+++ b/mlir/test/Dialect/Linalg/invalid.mlir
@@ -640,7 +640,7 @@
 func @illegal_fill_tensor_no_return(%arg0 : index, %arg1 : index, %arg2 : f32)
 {
   %0 = linalg.init_tensor [%arg0, %arg1] : tensor<?x?xf32>
-  // expected-error @+1 {{expected fill op with no result value to use memref type}}
+  // expected-error @+1 {{expected the number of results (0) to be equal to the number of output tensors (1)}}
   linalg.fill(%arg2, %0) : f32, tensor<?x?xf32>
 }
 
@@ -648,7 +648,7 @@
 
 func @illegal_fill_memref_with_return(%arg0 : memref<?x?xf32>, %arg1 : f32) -> memref<?x?xf32>
 {
-  // expected-error @+1 {{unexpected #results > #outputs}}
+  // expected-error @+1 {{expected the number of results (1) to be equal to the number of output tensors (0)}}
   %0 = linalg.fill(%arg1, %arg0) : f32, memref<?x?xf32> -> memref<?x?xf32>
   return %0 : memref<?x?xf32>
 }
@@ -658,7 +658,7 @@
 func @illegal_fill_memref_with_tensor_return
   (%arg0 : memref<?x?xf32>, %arg1 : f32) -> tensor<?x?xf32>
 {
-  // expected-error @+1 {{unexpected #results > #outputs}}
+  // expected-error @+1 {{expected the number of results (1) to be equal to the number of output tensors (0)}}
   %0 = linalg.fill(%arg1, %arg0) : f32, memref<?x?xf32> -> tensor<?x?xf32>
   return %0 : tensor<?x?xf32>
 }