After exiting the runway, the airplane was struck by a gust of wind and flipped over. The pilot was interviewed by a Federal Aviation Administration (FAA) inspector and stated that he had landed the airplane safely in crosswind conditions. As the airplane exited the runway, the wind shifted and he attempted to correct with full aileron and rudder input; however, his inputs were not successful and the airplane came to rest inverted. Airport personnel reported both wings, the tail, and vertical and horizontal stabilizers were damaged. They also indicated that the pilot reported that there were no mechanical issues with the airplane. Reported winds at the airport were from the northwest at 21 knots gusting to 38 knots. The pilot did not submit a written report.