The Italian, who won the final in Gstaad in 2018, has struggled with injury since reaching a career-high number six in May 2022.
He had lost his previous five meetings with the 12th-ranked Greek but edged the key moments in Switzerland to reach his second final of the year, following Marrakech in April.
He will face French qualifier Quentin Halys, ranked 192, who beat the German Jan-Lennard Struff 6-3, 7-6 (7/2) to make his first-ever ATP final.
Berrettini's return to form and fitness began with that win in Marrakech after which he progressed to the final in Stuttgart where he was beaten in three sets by Britain's Jack Draper.
He did not compete at the French Open but put up a good show in the second round at Wimbledon where he came second best to compatriot Jannik Sinner in a tight four-setter.