Prime Minister Shinzo Abe had earlier voiced relief, while still waiting for confirmation of the identity of the freed man.
Both Abe and foreign minister Taro Kono thanked Qatar and Turkey for their co-operation in freeing the man. A government spokesperson said that no ransom was paid for Yasuda's release.
"He looks to be in good health, but our staff will check his condition and transport him to Japan as soon as possible," Kono told reporters.
Yasuda's parents spoke to reporters outside their house near Tokyo.
"Above everything else, I want to see him being fine," said his father, Hideaki Yasuda.