The seventh seeds will start their campaign against Max Mirnyi and Alexander Bury of Belarus.
Paes, on the other hand, has been paired with a lower-ranked Vishnu Vardhan and the unseeded duo will start off against the Dutch team of Robin Hasse and Jean-Julien Rojer.
"I would love to play any of the Indian teams, but Bopanna and Bhupathi are closer to us in the draw," said Federer, who would be pairing with Stanislas Wawrinka to defend the men's doubles gold.
"I don't know why they (Bhupathi and Paes) didn't play together, but Bopanna is a very good player himself and I'msure on grass they will have a chance to do very well," added the Swiss, who won a record-equalling seventh Wimbledon title last month.
Federer, a strong favourite to win the singles gold after defending champion Rafael Nadal's injury-forced pullout, said getting the doubles gold is equally important for him.
"Obviously winning the Olympic gold with Stan in Beijing was one of the most incredible feelings I've ever had on atennis court," said Federer.
"Hopefully, we can do well again. We haven't played much doubles of late. Thank God we are seeded, that helped us out a little bit in the draw," he added.