Federer, the defending champ and a five-time winner of the event, earned a 6-2, 2-6, 6-4 triumph on Sunday to start Group B play. Rafael Nadal and American Mardy Fish will meet in the other Group B match later Sunday.
Only the top eight players qualified for the lucrative tournament at the O2 Arena in London.
The top two finishers from each round-robin group will advance to the semifinals.
Federer has been the hottest player of the eight, entering the tournament with a 12-match winning streak. He beat Tsonga for the Paris Masters crown last Sunday and also won in his native Basel the previous week, adding a couple of Davis Cup wins to his run of 10 straight ATP victories.
The seventh meeting of 2011 between Federer and Tsonga was dominated early by the Swiss superstar. Federer won the opening set in a mere 21 minutes, but the Frenchman returned the favor in a 30-minute second set.
A tight third set went on serve until the 10th game, when Federer won the first three points against Tsonga's serve. Tsonga managed to save one match point, but couldn't save the second to give Federer his 60th match win of 2011.
"In the first set, I didn't put one ball in the court, and that's it," said Tsonga. "Then I started playing better. I think he was a bit surprised, because I played so badly in the first set. It's better to start with a victory, but I'm still in the tournament and I will try to play my best tennis in the next match."