The 35-year-old Spanish legend won his second Australian Open title with 2-6, 6-7 (5-7), 6-4, 6-4, and 7-5 sets against world number 2 Medvedev, in almost five and a half hours of gameplay at Melbourne.
Nadal described the final as "one of the most emotional matches" of his career.
"Today I am here in front of all of you with this trophy. You don't know how much it means to be back here. You are amazing and thank you so much for all of your love and support," Nadal added.
Medvedev, 25, congratulated his opponent on the win.
"I want to congratulate Rafa because what he did today, I was amazed. You raised your level after two sets, won a 21st grand slam," he said.
"I'm going to try and be better next time," he added.
Before this game, Nadal, Novak Djokovic, and Roger Federer were all level on a men's record of 20 Grand Slam singles titles each.
Federer missed his chance to win the 21st title in the 2019 Wimbledon, losing to Djokovic.
Djokovic also failed to bag his 21st grand slam title after losing to Medvedev in the 2021 US Open final.
Djokovic was not allowed to participate in the 2022 Australian Open after his visa cancellation was upheld by a three-member bench of the Federal Court.
Medvedev lost his second Australian Open final after his first against Djokovic in 2021.
