The British No1 won the first set on a tie-break before taking the second 7-5. But Djokovic fought back to level the match and take the final to a deciding set.
However, Murray raced out of the blocks and stormed to victory in the final set, eventually sealing a 7-6 (12-10) 7-5 2-6 3-6 6-2 win and ending Britain’s 76-year wait for a Grand Slam singles winner.
“It means the world to me,” said Murray afterwards. “It’s what I’ve been working towards for the last 10 years of my life. Following the disappointment of the Wimbledon final a few months ago, to come back in the next Grand Slam is unbelievable.”
Murray is the first British man to win a Major singles title since Fred Perry, who won the US Open in 1936.
“When you’re on the court you don’t necessarily feel it, but when I was serving for the match there was a sense of how big a moment it was in British tennis history,” he continued.
“It’s something that hasn’t happened for a long time obviously in our country. And I’m obviously proud that I managed to achieve it.”
Murray, who also won Olympic gold at Wimbledon last month, admits he was overcome with emotion as he served out the victory.
“It was obviously very emotional,” he said. “I cried a little bit on the court. You’re not sad; you’re incredibly happy.
“I was in a little bit of disbelief because when I have been in that position many times before and not won, you do think, ‘is it ever going to happen?’
“Then when it finally does you’re obviously very, very excited. But mainly relieved to have got over that last hurdle.”