The 25-year-old Russian moved from fourth to third in the ATP's weekly list of rankings.
Djokovic's ninth title in Melbourne - his 18th crown at a Grand Slam tournament - will enable him to surpass Roger Federer's record of 310 weeks as number one.
Dominic Thiem dropped one place to fourth after his exit to Grigor Dimitrov in the last 16.
Medvedev and Thiem were the only changes in the men's top 10.
There was more movement at the top of the women's rankings.
The Australian Open champion Naomi Osaka swapped berths with Simona Halep to climb to second behind Ashleigh Barty. Osaka, 23, twice held top spot for a total of 25 weeks during 2019.
Serena Williams, beaten by Osaka on her run to the crown, rose four places to seventh.
Rise
Jennifer Brady, who lost Saturday's final in straight sets, reached a career high of 13.
“I think I belong at this level,” said the 25-year-old American following her defeat on Rod Laver Arena.
“I think winning a Grand Slam is totally achievable. It's within reach."
The Russian qualifier Aslan Karatsev boasted the most notable ascent.
The 27-year-old emerged from the qualifying tournament and knocked out three seeds, including Dimitrov, to advance to the semi-final where Djokovic halted his progress.
Karatsev began his run in Melbourne in 114th place in the world but his giant-killing feats catapulted him 72 places up the food chain into 42nd.
"Inside the top 50, I'm going to be able to go straight into the main draw and play bigger tournaments," he said.
"It's only the beginning of the year. There are still a lot of tournaments to play and a lot of training sessions to do. I'm going to attack this with more confidence."
