diff --git a/flang/include/flang/Optimizer/Transforms/CMakeLists.txt b/flang/include/flang/Optimizer/Transforms/CMakeLists.txt
--- a/flang/include/flang/Optimizer/Transforms/CMakeLists.txt
+++ b/flang/include/flang/Optimizer/Transforms/CMakeLists.txt
@@ -1,5 +1,8 @@
 
+set(LLVM_TARGET_DEFINITIONS RewritePatterns.td)
+mlir_tablegen(RewritePatterns.inc -gen-rewriters)
+add_public_tablegen_target(RewritePatternsIncGen)
+
 set(LLVM_TARGET_DEFINITIONS Passes.td)
 mlir_tablegen(Passes.h.inc -gen-pass-decls -name OptTransform)
 add_public_tablegen_target(FIROptTransformsPassIncGen)
-
diff --git a/flang/include/flang/Optimizer/Transforms/RewritePatterns.td b/flang/include/flang/Optimizer/Transforms/RewritePatterns.td
new file mode 100644
--- /dev/null
+++ b/flang/include/flang/Optimizer/Transforms/RewritePatterns.td
@@ -0,0 +1,59 @@
+//===-- RewritePatterns.td - FIR Rewrite Patterns -----------*- tablegen -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+///
+/// \file
+/// Defines pattern rewrites for fir optimizations
+///
+//===----------------------------------------------------------------------===//
+
+#ifndef FORTRAN_FIR_REWRITE_PATTERNS
+#define FORTRAN_FIR_REWRITE_PATTERNS
+
+include "mlir/IR/OpBase.td"
+include "mlir/Dialect/StandardOps/IR/Ops.td"
+include "flang/Optimizer/Dialect/FIROps.td"
+
+def IdenticalTypePred : Constraint<CPred<"$0.getType() == $1.getType()">>;
+def IntegerTypePred : Constraint<CPred<"fir::isa_integer($0.getType())">>;
+def IndexTypePred : Constraint<CPred<"$0.getType().isa<mlir::IndexType>()">>;
+
+def SmallerWidthPred
+    : Constraint<CPred<"$0.getType().getIntOrFloatBitWidth() "
+                       "<= $1.getType().getIntOrFloatBitWidth()">>;
+
+def ConvertConvertOptPattern
+    : Pat<(fir_ConvertOp (fir_ConvertOp $arg)),
+          (fir_ConvertOp $arg),
+          [(IntegerTypePred $arg)]>;
+
+def RedundantConvertOptPattern
+    : Pat<(fir_ConvertOp:$res $arg),
+          (replaceWithValue $arg),
+          [(IdenticalTypePred $res, $arg)
+          ,(IntegerTypePred $arg)]>;
+
+def CombineConvertOptPattern
+    : Pat<(fir_ConvertOp:$res(fir_ConvertOp:$irm $arg)),
+          (replaceWithValue $arg),
+          [(IdenticalTypePred $res, $arg)
+          ,(IntegerTypePred $arg)
+          ,(IntegerTypePred $irm)
+          ,(SmallerWidthPred $arg, $irm)]>;
+
+def createConstantOp
+    : NativeCodeCall<"$_builder.create<mlir::ConstantOp>"
+                     "($_loc, $_builder.getIndexType(), "
+                     "rewriter.getIndexAttr($1.dyn_cast<IntegerAttr>().getInt()))">;
+
+def ForwardConstantConvertPattern
+    : Pat<(fir_ConvertOp:$res (ConstantOp:$cnt $attr)),
+          (createConstantOp $res, $attr),
+          [(IndexTypePred $res)
+          ,(IntegerTypePred $cnt)]>;
+
+#endif // FORTRAN_FIR_REWRITE_PATTERNS
diff --git a/flang/lib/Optimizer/Dialect/FIROps.cpp b/flang/lib/Optimizer/Dialect/FIROps.cpp
--- a/flang/lib/Optimizer/Dialect/FIROps.cpp
+++ b/flang/lib/Optimizer/Dialect/FIROps.cpp
@@ -24,6 +24,9 @@
 #include "llvm/ADT/StringSwitch.h"
 #include "llvm/ADT/TypeSwitch.h"
 
+namespace {
+#include "flang/Optimizer/Transforms/RewritePatterns.inc"
+} // namespace
 using namespace fir;
 
 /// Return true if a sequence type is of some incomplete size or a record type
@@ -772,7 +775,11 @@
 //===----------------------------------------------------------------------===//
 
 void fir::ConvertOp::getCanonicalizationPatterns(
-    OwningRewritePatternList &results, MLIRContext *context) {}
+    OwningRewritePatternList &results, MLIRContext *context) {
+  results.insert<ConvertConvertOptPattern, RedundantConvertOptPattern,
+                 CombineConvertOptPattern, ForwardConstantConvertPattern>(
+      context);
+}
 
 mlir::OpFoldResult fir::ConvertOp::fold(llvm::ArrayRef<mlir::Attribute> opnds) {
   if (value().getType() == getType())
diff --git a/flang/lib/Optimizer/Transforms/CMakeLists.txt b/flang/lib/Optimizer/Transforms/CMakeLists.txt
--- a/flang/lib/Optimizer/Transforms/CMakeLists.txt
+++ b/flang/lib/Optimizer/Transforms/CMakeLists.txt
@@ -9,6 +9,7 @@
   FIRDialect
   FIRSupport
   FIROptTransformsPassIncGen
+  RewritePatternsIncGen
 
   LINK_LIBS
   FIRDialect
diff --git a/flang/test/Fir/convert-fold.fir b/flang/test/Fir/convert-fold.fir
new file mode 100644
--- /dev/null
+++ b/flang/test/Fir/convert-fold.fir
@@ -0,0 +1,37 @@
+// RUN: fir-opt --canonicalize %s | FileCheck %s
+
+// CHECK-LABEL: @ftest
+func @ftest(%x : i1) -> i1 {
+  // this pair of converts should be folded and DCEd
+  %1 = fir.convert %x : (i1) -> !fir.logical<1>
+  %2 = fir.convert %1 : (!fir.logical<1>) -> i1
+  // CHECK-NEXT: return %{{.*}} : i1
+  return %2 : i1
+}
+
+// CHECK-LABEL: @gtest
+func @gtest(%x : !fir.logical<2>) -> !fir.logical<2> {
+  // this pair of converts should be folded and DCEd
+  %1 = fir.convert %x : (!fir.logical<2>) -> i1
+  %2 = fir.convert %1 : (i1) -> !fir.logical<2>
+  // CHECK-NEXT: return %{{.*}} : !fir.logical<2>
+  return %2 : !fir.logical<2>
+}
+
+// CHECK-LABEL: @htest
+func @htest(%x : !fir.int<4>) -> !fir.int<4> {
+  // these converts are NOPs and should be folded away
+  %1 = fir.convert %x : (!fir.int<4>) -> !fir.int<4>
+  %2 = fir.convert %1 : (!fir.int<4>) -> !fir.int<4>
+  // CHECK-NEXT: return %{{.*}} : !fir.int<4>
+  return %2 : !fir.int<4>
+}
+
+// CHECK-LABEL: @ctest
+func @ctest() -> index {
+  %1 = constant 10 : i32
+  %2 = fir.convert %1 : (i32) -> index
+  // CHECK-NEXT: %{{.*}} = constant : index
+  // CHECK-NEXT: return %{{.*}} : index
+  return %2 : index
+}