There had been widespread speculation that the two superstars would play together in Brazl.
Hingis, 35, had reportedly made the offer to play with Federer and was waiting for a response from the winner of 17 Grand Slam titles.
"I`m very excited about that because I haven`t played with Martina I guess in 15 years," said Federer.
The report added that Federer would also play the Rio 2016 men's doubles tournament alongside countryman Stan Wawrinka.
Hingis will contest the women's doubles with Belinda Bencic, the reports said.