The second-seeded Tsitsipas saved all three break points he faced to beat Bonzi of France 6-4, 6-4.
Tsitsipas, ranked sixth, will be seeking his second title of the season after defending his Monte Carlo championship in April. The final will be the first on grass at the tour level for the Greek player.
Tsitsipas said that, win or lose the final, he believes he has had ideal preparation for Wimbledon next week.
"I have played a final a week before a Grand Slam before," he said. "It was the year I made the final at Roland Garros, in Lyon. It worked out pretty well to have that final and consistency of matches."