The Latvian was the first wildcard to reach the final since Daniela Hantuchova in 2000 and kept up her good form ahead of Wimbledon by beating Kontaveit 6-3 6-3.
French Open 2017 winner Ostapenko dominated from the start and picked up the victory in one hour and five minutes, adding to her three previous career WTA titles.
She has now won titles on all four surfaces – clay, hard, indoor and grass – and is hopeful of improving on her current world ranking of No.43.
"I think it says that I can be dangerous and playing well on all surfaces probably," she said after the victory.
"Of course I enjoy to play more on just some of them, but in general I can adjust well to different surfaces.
"I think this is just the beginning for me. If I keep playing the way I played this tournament, I think I can be back in top 10 and play well.
"I just have to keep that in my mind and work even harder."
Ostapenko made good use of her strong service game to break Kontaveit's serve in the third and fifth games.
Kontaveit earned a first break in the eighth game with four service return winners in a row, but Ostapenko recovered from 40-15 in the next game to take the opening set.
It was then plain sailing for Ostapenko in the second set as she earned the only break at 2-1 and held for the remainder, clinching the victory with her second championship point.
Ostapenko will face Leylah Fernandez in the first round of Wimbledon next week.