Tsonga won 6-3 6-3 in 73 minutes to set up a showdown with Diego Schwartzman after the Argentinian beat Greece's Stefanos Tsitsipas 6-3 7-5 in the other semi-final.
"Ruben had played a few good matches before and he was pretty confident, so it was not easy," Tsonga told the ATP website. "I played well and had to play my best tennis to win."
"I didn't play for a few weeks because of my knee injury and now I'm coming back and I play a new final here. For me it's great and I hope I will be able to hold the trophy."
It was a historic day at the Kremlin Cup in Moscow, with two Bosnians playing in the semi-final of an ATP World Tour event for the first time.
And it was sixth seed Damir Dzumhur who came out on top with a 6-0 7-6 (11/9) victory over his good friend and qualifier Mirza Basic, who had not reached a tour-level quarter-final before this week.
"It means a lot for Bosnian tennis. It means a lot for Bosnian people," Dzumhur said. "I think back home in Bosnia everyone was watching us today."
Dzumhur, who won the St Petersburg Open in September, will face Ricardas Berankis in the final after the Lithuanian came from a set down to beat Adrian Mannarino 3-6 6-4 6-1.