The second-seeded Frenchman, who was playing his first final on the red dirt, held serve throughout and broke decisively in the last game to clinch his 15th ATP title.
Tsonga's victory on the eve of the claycourt major raised hopes that he may finally end the country's 34-year search for a homegrown male champion at Roland Garros. Yannick Noah was the last Frenchman to lift the Musketeers' Cup in 1983.
Tsonga reaches maiden final on clay
Tsonga had gotten off to a poor start in the claycourt season, withdrawing from his second-round match at the Madrid Masters before skipping the Rome Masters with a shoulder injury.
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He seems to have recovered well as he produced a solid performance against third seed Berdych, who never found the key to the Frenchman's service.
The Czech had to set points at 5-4 40-15 on Tsonga's serve, but like he did all week, Tsonga played the big points perfectly.
"It was a very close match. I had a very big chance at the end of the first set when I had two set points, and I think that was the key of the match," said Berdych.
"To win the set, it would put me in a completely different position, but Jo was able to save that, hold that, and I didn't really create many chances after that."
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