The Italian fourth seed was blown off course in the first two sets but recovered to win 3-6, 3-6, 6-4, 6-4, 6-3 in three hours and 44 minutes.
"We're trying to get better every day," he said of his team after becoming the youngest Melbourne Park champion since Djokovic in 2008.
"Even during the tournament we try to get stronger, trying to understand every situation a little bit better.
"I'm so glad to have you there supporting me, understanding me which sometimes is not easy because I'm still a little bit young sometimes. But it is what it is."
The result is a bitter blow for Medvedev, who became the first player to ever lose two Grand Slam finals from two sets up, after falling to Rafael Nadal here two years ago.
"It's been honestly an amazing two weeks. It always hurts to lose in the final but probably being in the final is better than losing before," Medvedev said at the trophy ceremony.
"I always want to win but I guess I have to try harder next time. But I'm proud of myself, I'm going to try even harder next time."
Medvedev had also the first man since Pete Sampras almost three decades ago to reach the final after multiple comebacks from two sets down and he came out of the blocks all guns firing, as his aggressive mindset and approach totally rattled his opponent, who was in his first Grand Slam final.
The Italian, playing in his first Grand Slam final, was broken just twice in the entire tournament in the run-up to Sunday's title decider but Medvedev doubled that tally in the first set.
World number four Sinner was again in deep trouble at the start of the second set, fending off multiple break points against a hungry Medvedev and pleading for backing from the crowd on Rod Laver Arena.
He survived that onslaught but was broken for a third time in the match in the fourth game when a poor drop shot allowed the Russian to set up a winner.
Medvedev raced through his service game to love, giving Sinner no time to gather his thoughts.
He hit a fierce forehand to set up two more break points in the sixth game and Sinner went wide with a forehand to slip 5-1 down.
The Italian broke back immediately and had another break point in the ninth game to put the set back on serve but Medvedev snuffed out the mini-revival.
The third set was tighter and went with serve until the decisive 10th game.
Sinner put a forehand passing shot wide at the end a 31-shot rally, missing out on the chance to earn two set points, but his chance came again and this time he took it to seal the set.
The momentum was now with Sinner and Medvedev, who required strapping for his foot, had to fight hard to hold early in the fourth set.
Sinner fired three aces to edge 4-3 ahead and broke in the 10th game when Medvedev fired long to take the match into a fifth set.
With the tension mounting, both players stayed solid on serve until the sixth game, when Medvedev dumped a backhand into the net to give Sinner three break points.
A forehand crosscourt winner gave the Italian the crucial break and he went on to take his first championship point, becoming the first Italian since Adriano Panatta in 1976 to win a major.
He celebrated by dropping to his back on the blue court before climbing into the stands to embrace his team.
