The easiest way - take the hinges off and move them to the outside of the door frame. (Assuming you wont mind the old hinge mortises showing inside the closet.) You'll probably also have to move the stop molding in the door frame (the trim that the door closes against.)
Or you can completely remove the door AND the door frame, and turn it around - a bigger & messier job, but would probably end up looking better.
It depends on the door frame ... you'll have to decide what's easiest for you (e.g. is the molding held on with 50 years of paint?...)