We investigate the relaxation of rectangular wrinkled thin films intrinsically containing an initial strain gradient. A preferential rolling direction, depending on wrinkle geometry and strain gradient, is theoretically predicted and experimentally verified. In contrast to typical rolled-up nanomembranes, which bend perpendicular to the longer edge of rectangular patterns, we find a regime where rolling parallel to the longer edge of the wrinkled film is favorable. A nonuniform radius of the rolled-up film is well reproduced by elasticity theory and simulations of the film relaxation using a finite element method.