Defending champion Rublev, bidding for a second straight title in Dubai, was unable to put up much resistance as he was beaten 6-2 6-2 in a battle between childhood friends that lasted just over an hour.
Medvedev, who entered the final having not dropped a set this week, added to last month's titles in Doha and Rotterdam to take his tally to 19 Tour-level titles.
"It is 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," Medvedev said.
"I was really happy with these three weeks and I am looking forward to the next ones.
"I know Andrey can cause a lot of trouble to everyone on Tour. 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."
The 27-year-old, who sent down nine aces and converted 57% of the breakpoints he won in the final, moves sixth in the ATP rankings, while Rublev drops to number seven.
"I think it's a good thing for Daniil that he's doing this, for his career, for his life, that he's achieving those things. Three titles in a row, it's unreal. What else to say?" Rublev told a post-match news conference.
Former U.S. Open champion Medvedev next travels to the United States where he will look to continue his winning run at Indian Wells from March 8th to March 19th.
