Top seed Djokovic won 7-5 6-2 6-2 to claim his 18th Grand Slam, leaving him two behind Roger Federer and Rafael Nadal in the men’s record books.
The 33-year-old Serb has never lost a final at Melbourne Park and beating Medvedev is a third triumph in a row.
Russian fourth seed Medvedev, 25, has lost both of his Grand Slam finals.
After losing to Nadal in the 2019 US Open final, the Russian was tipped to push Djokovic close and win his maiden major.
Medvedev had reached the Melbourne final on the back of a 20-match winning streak, but floundered under the intense pressure applied by Djokovic.
Throwing racquets, poor body language and shouting angrily at his team were an illustration of how the Russian imploded in the third set, contrasting starkly with Djokovic’s confident and steely exterior.