diff --git a/flang/include/flang/Optimizer/Dialect/FIROps.td b/flang/include/flang/Optimizer/Dialect/FIROps.td
--- a/flang/include/flang/Optimizer/Dialect/FIROps.td
+++ b/flang/include/flang/Optimizer/Dialect/FIROps.td
@@ -33,8 +33,6 @@
     "FIR dialect type">;
 
 // Fortran intrinsic types
-def fir_ComplexType : Type<CPred<"$_self.isa<fir::ComplexType>()">,
-    "FIR complex type">;
 def fir_IntegerType : Type<CPred<"$_self.isa<fir::IntegerType>()">,
     "FIR integer type">;
 def fir_LogicalType : Type<CPred<"$_self.isa<fir::LogicalType>()">,
diff --git a/flang/include/flang/Optimizer/Dialect/FIRType.h b/flang/include/flang/Optimizer/Dialect/FIRType.h
--- a/flang/include/flang/Optimizer/Dialect/FIRType.h
+++ b/flang/include/flang/Optimizer/Dialect/FIRType.h
@@ -42,7 +42,6 @@
 using KindTy = unsigned;
 
 namespace detail {
-struct ComplexTypeStorage;
 struct HeapTypeStorage;
 struct IntegerTypeStorage;
 struct LenTypeStorage;
@@ -95,21 +94,6 @@
 
 // Intrinsic types
 
-/// Model of a Fortran COMPLEX intrinsic type, including the KIND type
-/// parameter. COMPLEX is a floating point type with a real and imaginary
-/// member.
-class ComplexType : public mlir::Type::TypeBase<fir::ComplexType, mlir::Type,
-                                                detail::ComplexTypeStorage> {
-public:
-  using Base::Base;
-  static fir::ComplexType get(mlir::MLIRContext *ctxt, KindTy kind);
-
-  /// Get the corresponding fir.real<k> type.
-  mlir::Type getElementType() const;
-
-  KindTy getFKind() const;
-};
-
 /// Model of a Fortran INTEGER intrinsic type, including the KIND type
 /// parameter.
 class IntegerType : public mlir::Type::TypeBase<fir::IntegerType, mlir::Type,
diff --git a/flang/include/flang/Optimizer/Dialect/FIRTypes.td b/flang/include/flang/Optimizer/Dialect/FIRTypes.td
--- a/flang/include/flang/Optimizer/Dialect/FIRTypes.td
+++ b/flang/include/flang/Optimizer/Dialect/FIRTypes.td
@@ -83,7 +83,30 @@
   let parser = [{
     return get(context);
   }];
+}
+
+def fir_ComplexType : FIR_Type<"Complex", "complex"> {
+  let summary = "Complex type";
+
+  let description = [{
+    Model of a Fortran COMPLEX intrinsic type, including the KIND type
+    parameter. COMPLEX is a floating point type with a real and imaginary
+    member.
+  }];
+
+  let parameters = (ins "KindTy":$fKind);
 
+  let printer = [{
+    $_printer << "complex<" << getFKind() << '>';
+  }];
+
+  let genAccessors = 1;
+
+  let extraClassDeclaration = [{
+    using KindTy = unsigned;
+
+    mlir::Type getElementType() const;
+  }];
 }
 
 def ShapeType : FIR_Type<"Shape", "shape"> {
diff --git a/flang/lib/Optimizer/Dialect/FIRType.cpp b/flang/lib/Optimizer/Dialect/FIRType.cpp
--- a/flang/lib/Optimizer/Dialect/FIRType.cpp
+++ b/flang/lib/Optimizer/Dialect/FIRType.cpp
@@ -58,11 +58,6 @@
   return TYPE::get(ty);
 }
 
-// `complex` `<` kind `>`
-fir::ComplexType parseComplex(mlir::DialectAsmParser &parser) {
-  return parseKindSingleton<fir::ComplexType>(parser);
-}
-
 // `slice` `<` rank `>`
 SliceType parseSlice(mlir::DialectAsmParser &parser) {
   return parseRankSingleton<SliceType>(parser);
@@ -309,7 +304,7 @@
   if (typeNameLit == "char")
     return generatedTypeParser(dialect->getContext(), parser, typeNameLit);
   if (typeNameLit == "complex")
-    return parseComplex(parser);
+    return generatedTypeParser(dialect->getContext(), parser, typeNameLit);
   if (typeNameLit == "field")
     return generatedTypeParser(dialect->getContext(), parser, typeNameLit);
   if (typeNameLit == "heap")
@@ -440,30 +435,6 @@
   explicit IntegerTypeStorage(KindTy kind) : kind{kind} {}
 };
 
-/// `COMPLEX` storage
-struct ComplexTypeStorage : public mlir::TypeStorage {
-  using KeyTy = KindTy;
-
-  static unsigned hashKey(const KeyTy &key) { return llvm::hash_combine(key); }
-
-  bool operator==(const KeyTy &key) const { return key == getFKind(); }
-
-  static ComplexTypeStorage *construct(mlir::TypeStorageAllocator &allocator,
-                                       KindTy kind) {
-    auto *storage = allocator.allocate<ComplexTypeStorage>();
-    return new (storage) ComplexTypeStorage{kind};
-  }
-
-  KindTy getFKind() const { return kind; }
-
-protected:
-  KindTy kind;
-
-private:
-  ComplexTypeStorage() = delete;
-  explicit ComplexTypeStorage(KindTy kind) : kind{kind} {}
-};
-
 /// `REAL` storage (for reals of unsupported sizes)
 struct RealTypeStorage : public mlir::TypeStorage {
   using KeyTy = KindTy;
@@ -779,18 +750,6 @@
 
 KindTy fir::IntegerType::getFKind() const { return getImpl()->getFKind(); }
 
-// COMPLEX
-
-fir::ComplexType fir::ComplexType::get(mlir::MLIRContext *ctxt, KindTy kind) {
-  return Base::get(ctxt, kind);
-}
-
-mlir::Type fir::ComplexType::getElementType() const {
-  return fir::RealType::get(getContext(), getFKind());
-}
-
-KindTy fir::ComplexType::getFKind() const { return getImpl()->getFKind(); }
-
 // REAL
 
 RealType fir::RealType::get(mlir::MLIRContext *ctxt, KindTy kind) {
@@ -1081,11 +1040,6 @@
 void fir::printFirType(FIROpsDialect *, mlir::Type ty,
                        mlir::DialectAsmPrinter &p) {
   auto &os = p.getStream();
-  if (auto type = ty.dyn_cast<fir::ComplexType>()) {
-    // Fortran intrinsic type COMPLEX
-    os << "complex<" << type.getFKind() << '>';
-    return;
-  }
   if (auto type = ty.dyn_cast<RecordType>()) {
     // Fortran derived type
     os << "type<" << type.getName();
@@ -1328,3 +1282,16 @@
   }
   printer << '>';
 }
+
+//===----------------------------------------------------------------------===//
+// ComplexType
+//===----------------------------------------------------------------------===//
+
+mlir::Type fir::ComplexType::parse(mlir::MLIRContext *context,
+                                   mlir::DialectAsmParser &parser) {
+  return parseKindSingleton<fir::ComplexType>(parser);
+}
+
+mlir::Type fir::ComplexType::getElementType() const {
+  return fir::RealType::get(getContext(), getFKind());
+}