French 13th seed Tsonga hit 11 aces and 26 winners to win Sunday's final 7-5, 7-6 (7/3) while Federer, two days after his 33rd birthday, was undone by 37 unforced errors.
"If you believe in something it can happen," said Tsonga.
"I'm proud of what I've achieved this week," he said.
"I played well all this week — I beat many good guys."
The 29-year-old Tsonga dropped just one set all week as he knocked out world number one Novak Djokovic and Andy Murray en route to the final.
It was Tsonga's second career Masters 1000 title, coming almost six years after his first at Paris Bercy in 2008.
He is just the second French player after Guy Forget to win two titles at the Masters level.
Tsonga spent just over one and three-quarter hours in constructing his upset over the man who had beaten him in both of their previous finals played in 2011.
Tsonga dealt with injuries for much of 2013 but is now fit and brimming with confidence.
The French player said his win Sunday had special significance because of his experience two years earlier.
Fresh off winning an Olympic silver medal in doubles in the 2012 London
Games, Tsonga injured his right knee in Toronto after walking into a fire hydrant as he was out for a stroll. He had lost in the opening round of the Masters 1000 event in Toronto to Jeremy Chardy.
The injury required eight stitches and forced him to pull out of the Cincinnati Masters event the following week.
"This will stay in my heart forever," Tsonga said.
"Two years ago here I had knee problems, now it's all changed," he said.
"This win was something really special — I have a lot of respect for Roger."
Federer, the second seed, had been bidding for his 80th career title and 300th win at a Masters.
The Swiss star was playing his sixth final of the season and has won titles in Dubai and Halle.
He has also lost in the final at Wimbledon.
"I had a great time, even if the match didn't go as I was hoping," said Federer, now 44-9 this season as he heads to Cincinnati next week.
"I had some epic night sessions this week, and I really enjoyed them," he said.
"Jo deserved this title, he beat some amazing players on the way and backed it up with another title."