The former world number one, who ended Novak Djokovic's 20-match win streak in the semi-finals, triumphed 6-2, 6-2 over the defending champion.
Medvedev arrived in Dubai on the back of successive titles in Rotterdam and Qatar.
"It's amazing because at the start of the year, it was not perfect. In tennis when you don't win matches you have doubts. Now it just feels better," said Medvedev, who took his own winning streak to 14.
Medvedev now has 18 tour titles and is the third player to win three titles in as many weeks since 2021, joining Casper Ruud (July 2021) and Felix Auger-Aliassime (October 2022).
"I was really happy with these three weeks and I am looking forward to the next ones."
The 27-year-old added: "It was very tactical match. I know Andrey can cause a lot of trouble to everyone. Every time we play he tries to make me suffer, I try to make him suffer.
"Today I managed to be on top, but the next match could be a different story."
