Second seed Medvedev, 25, lost his two previous Grand Slam finals but was composed throughout a 6-4 6-4 6-4 win.
World number one Djokovic had already won the Australian Open, French Open and Wimbledon titles this year.
The 34-year-old Serb was also chasing a record 21st Grand Slam men’s title.
Victory would have moved him clear of rivals Roger Federer and Rafael Nadal in the battle to finish with the most men’s majors, but it was the potential calendar Grand Slam which Djokovic had said would be the “greatest achievement” of his career.
Perhaps burdened by the weight of history, Djokovic looked subdued throughout as he made a high number of uncharacteristic errors and also became tearful towards the end.
He also looked way short of his usual physical capabilities.
To put those factors down as the sole reasons for Medvedev’s success would be completely wrong.
The Russian played smartly and confidently, drawing the errors out of his opponent with strong serving and finishing points with precise winners, as he avenged a straight-set defeat by Djokovic in February’s Australian Open final.
There was a slight wobble as he tried to serve out for the title – three double faults helped Djokovic nick back a break for 5-3 – before Medvedev composed himself to take his third championship point.
After sharing a warm hug with Djokovic at the net, Medvedev broke out in a broad smile before sitting back in his chair to contemplate finally winning the first Grand Slam title which he has long threatened.
“I want to thank my team, those who are here and watching. My parents, my family, my sisters. Some of my friends are here too,” said Medvedev, who dropped only one set in the tournament.
“Thank you guys because it is not an easy journey to win a Slam. I’m really thankful to you for helping me throughout this journey.”
Addressing Medvedev, Djokovic said: “If there is anyone who deserves a Grand Slam title right now, it is you. Well done. There will be many more titles to come, I’m sure.”
Two years ago, Medvedev cut an emotional figure after the men’s singles final in New York.
It was the Russian’s first Grand Slam final and, after an exhilarating fightback from two sets down, he eventually lost an epic five-setter to Nadal.
Mesmerised by a video montage on the Ashe television screens showing all of Nadal’s achievements – then standing at 19 Grand Slam titles – the Russian later said he wanted to use that as further inspiration in his own quest to land the sport’s biggest prizes.
Finally he has achieved that.
In Melbourne on his second attempt, Medvedev was overwhelmed by the intense pressure from Djokovic and his game broke down.
This time, it was a complete role reversal.
Medvedev broke in the first game of the match and while Djokovic settled down in his service games in the rest of the set, the problem was he could make no impact on the Russian’s serve.
Firing them down with pace and precision meant even the best returner in the men’s game had no answers. (Courtesy BBC)