Other answers do not mention "dynamic" type. So to add one more answer, you can use "dynamic" type to store your resulting object without having to cast converted object with a static type.
dynamic changedObj = Convert.ChangeType(obj, typeVar);
changedObj.Method();
Keep in mind that with the use of "dynamic" the compiler is bypassing static type checking which could introduce possible runtime errors if you are not careful.
Also, it is assumed that the obj is an instance of Type typeVar or is convertible to that type.