The 13th-seeded Frenchman won his first ATP Tour title of the season and 11th overall. He beat top-ranked Novak Djokovic on Thursday, eighth-seeded Andy Murray on Friday and seventh-seeded Grigor Dimitrov on Saturday.
Tsonga improved to 5-11 against Federer.
Federer dropped to 2-5 in finals this season, with his victories coming in Dubai and Halle.
The Swiss star made several uncharacteristic errors and had a hard time with Tsonga’s powerful serve and ground strokes.
The first set was a rather choppy affair.
Both players made some unforced errors over the first few games, but each held serve.
Tsonga struggled with his first serve midway through the set, though his spin-heavy second serve was effective.
The quality of the match picked up late in the set. With Tsonga serving at 5-5, Federer showed his skills at the net with a deft drop shot that a Tsonga could not retrieve.
The Frenchman held to put the pressure back on Federeer. Federer struggled in the final game, spraying two shots long to fall behind 30-15. He pulled even with a winner, but was wide with a groundstroke that was unsuccessfully challenged, setting up the first break point opportunity of the set. Federer launched a ball well long to give Tsonga the opening set in 44 minutes.
Tsonga kept the pressure on in the second set and had a break point chance with a 3-2 lead. Federer answered with an ace and fought back for the hold.
Tsonga then had a great chance with a 4-3 lead in the second set and a double-break point. However, Federer answered with two straight points to get to deuce. Tsonga had two more break point chances later in the game, but Federer saved them both and then held with an ace.
In the tiebreaker, Tsonga picked up a mini-break at 4-3 and took the next three points for the victory.
In the doubles final, Bruno Soares Alexander Peya topped Ivan Dodig and Marcelo Meloof 6-4, 6-3.