"This has been one of the greatest weeks of my life," Kyrgios said. "I've made massive strides. This is a tournament I'm definitely going to play for the rest of my life."
Both men served dominantly during the encounter. Neither player faced a break point or lost more than two points while serving.
Medvedev, 23, will rise to a career best ninth on the ATP rankings following his run to the final.
Success for Kyrgios will propel him 25 places up the ladder to 27 in the world and a first appearance in the top 30 in 10 months for the 24-year-old.
"I know how well Nick can play when he wants to play," Medvedev said. "This week, I think he wanted to play and it was tough."