The announcement was made by Japanese Defence Minister Takeshi Iwaya, however the FDR has suffered "severe damage", and is missing key parts to it, including the storage device that records flight time, speed and altitude.
A team working from the deep-sea search vessel Van Gogh, which is currently being chartered by the US Navy, made the discovery nearly a week ago in the western Pacific, near the presumed crash site.
Minister Iwaya said that the search would continue for the pilot and the rest of the aircraft, as well as the missing parts to the FDR.
The pilot was flying with three other F-35s when he lost contact and disappeared off radar about 140 kilometres east of Misawa Air Base, however locating the aircraft and the pilot is proving to be very difficult, with the suspected crash zone estimated to be 5,000 feet deep.
Japan is currently deploying a rescue submarine, among other vessels, to try and find the F-35.
Since the aircraft crashed off the north of Japan, the race has been on to salvage the wreck, in order to protect/reveal the technology inside the fifth-generation fighter.