Federer, the Swiss superstar and defending champ, beat the Frenchman 6-2, 2-6, 6-4 to kick off Group B play at the event, continuing a 12-match winning streak that has included victories at Basel and the Paris Masters.
Federer breezed through the opening set in just 21 minutes, but Tsonga returned the favor in the middle frame, taking the set in 30 minutes.
Federer then won the first three points of the final set against Tsonga's serve and went on to claim his 60th match of 2011.
Meanwhile, Nadal of Spain edged American Mardy Fish 6-2, 3-6, 7-6 (7-3) in the day's other Group B match at London's O2 Arena.
Nadal double-faulted five times but still managed to overcome seven Fish aces by saving 8-of-11 break points.
Fish and Tsonga will play Tuesday, while Nadal will take on Federer.
Group A starts play Monday. World No. 1 Novak Djokovic will face Czech Tomas Berdych while British star Andy Murray will go up against Spaniard David Ferrer.