The 25-year-old overcame Djokovic 7-6 7-5 2-6 3-6 6-2 to win his first ever Grand Slam final at the fifth time of asking.
"It wasn't to be but I want to congratulate Andy for his first Grand Slam, he absolutely deserves it," said Djokovic. "Also, his team, this is your success also.
"I would like to thank my team, my family and friends for supporting me. I tried my best. I gave it my all and it was another tremendous match to be a part of. It was definitely enjoyable."
Murray won 160 points in the match - five more than his opponent.