Davydenko, a former No. 3 who has dropped to 44th in the world, beat top-seeded David Ferrer 6-2, 6-3. The second-seeded Gasquet overcame German qualifier Daniel Brands 7-5, 7-5.
Davydenko broke Ferrer to go up 2-1 and then again to make it 5-2, winning 13 of 14 points in one stretch. Ferrer, was uncharacteristically sloppy, hitting only two winners and making 15 unforced errors.
"I waited already a long time to reach a final. Last season was pretty tough and the best result was a semifinal," said Davydenko, who beat Rafael Nadal to win the 2010 Qatar tournament. "Now in my first tournament, I'm in a final so happy."
With the win, Davydenko improved to 4-2 against Ferrer.
"He played better than me all the time," Ferrer said. "He served better. He received better. He was better. I didn't have any chance in the match."
In the early match, the 10th-ranked Gasquet struggled early against the big-hitting German. Brands controlled the rallies with his forehand, often pushing Gasquet beyond the baseline. But as the first set went on, the Frenchman started mixing up his shots and serving better.
The second set was just as tight, with Brands saving a break point to even the set at 3-3. But Gasquet continued his strong serving, hitting an ace to go up 5-4 and another good serve to lead 6-5. Gasquet broke the 153rd-ranked Brands with a backhand winner for the victory and a chance to claim his eighth title.
"He was very powerful, serving the forehand. So very talented," Gasquet said. "I was mentally tough, and I played well."
Gasquet, who last year won his seventh title in Bangkok and reached the top 10 for the first time since 2007, said he is feeling fit.
"Tomorrow I have to win this final, but, yeah, it's true, I'm feeling well," Gasquet said. "I don't know what I can do this year. But on every match I will try to fight, and I will try to prepare better on Grand Slams, to win some tournaments, to start in Doha in the final, so it's important to win."