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.
Djokovic was bidding to become just the sixth player to win a calendar Slam and the first man to do it since Rod Laver in 1969.
The Russian played smartly and confidently, drawing the errors out of his opponent with strong serving, dominating his opponent from the baseline and finishing points with precise winners, as he avenged a straight-set defeat by Djokovic in February’s Australian Open final.