The victory finally handed the Scot his first Grand Slam title, having previously reached four finals before last night's contest.
Murray, who won gold in the Olympic men's singles tournament earlier this summer, defeated Djokovic 7-6 (12-10) 7-5 2-6 3-6 6-2 in a match lasting four hours 54 minutes in the Arthur Ashe Stadium.
He ends Britain's 76-year wait to find a Grand Slam champion, after Fred Perry last won a title in 1936.
Sir Sean Connery, Sir Alex Ferguson, Kevin Spacey and Sir Patrick Stewart were among the celebrities who watched the final inside the stadium last night.
With Murray finishing his match after 2am UK time, he has since been congratulated by various celebrities and sports stars.
David Cameron: "Delighted Andy Murray is continuing a golden summer of sport by winning the US Open. A truly great victory."
Jonathan Ross: "I had to bail out before the last set, but incredible victory for Andy Murray. So well deserved."
Simon Pegg: "Many congrats to Andy Murray in New York this morning and much love to New York City too while we're at it."
Gary Lineker: "Congratulations to @andy_murray on a superb US Open victory. Something immensely satisfying in proving people wrong. #winner".
Coldplay: "@andy_murray Massive congratulations. What a champion."
Robbie Savage: "Congratulations @andy_murray gotta be #spoty now ..surely '"
Rio Ferdinand: "How could my twitter not work last night? Congrats @andy_murray, won a Grand Slam title..I think the boss [Sir Alex Ferguson] gave u the hair dryer! #inspired."
Niall Horan (One Direction): "ive never seen a game of tennis like this in my life! unbelievable! murray wrap it up dude."
David Walliams: "Andy Murray not only won his first Grand Slam, he had Sir Sean Connery cheering him on. #jamesbondhelpedAndywin"
Laura Robson: "Us Open Champion Andy Murray. So happy for him. #proud"
Kevin Spacey: "Congratulations @Andy_Murray on your well deserved, brilliant win at US Open. I cheer your victory & everyone back home is so happy for you!"
Ewan McGregor: "Murray wins historic first major!!"
Kevin McHale (Glee): "Congrats Andy Murray!! Such an incredible match!"
Jamie Murray (Andy's brother): "Thank you to everybody for their kind messages and support of Andy :) An amazing night!"
Calvin Harris: "ANDY MURRAY YOU ABSOLUTE SCOTTISH HERO #SCOTTISH #TENNIS #LEGEND"
Bill Bailey: "Andy Murray! Fantastically well done! Amazing scenes.. Ivan Lendl's face moved a little bit!"
Tom Hiddleston: "Andy Murray isn't the next Fred Perry. He's the first Andy Murray. An exceptional display of both strength and will. A champion."
Russell Crowe: "Andy Murray on a roll. You champion."
Jack Whitehall: "Sports Personality of the Year?? Wiggins? Hoy? Murray? I think it's safe to say Joey Barton can put that tuxedo away."
Dara O'Briain: "So happy for Andy Murray. Hope he wins many, many more..."
Jimmy Carr: "Andy Murray has just made me cry. The man is a God. I'm so happy."
Gary Lightbody (Snow Patrol): "Yes yes yes! Joy! Andy Murray US Open champion! Incredible match! Well done Andy. Historic, emotional and so well deserved!"
Piers Morgan: "Absolutely magnificent win by @andy_murray - what heart, what fight, what guts. #PrideofBritain"
Alan Davies: "Djokovic comes round to hug Murray. Amazing final. Amazing win. That was so tough."
Ant & Dec: "Yessssssssss! Andy Murray!! Immense. Proud of you! Dx #usopen"
Stephen Fry: "Glory glory glory glory glory GLORY be!!! Andy Murray, you beauty! #USOpen"
Sir Clive Woodward
"@andy_murray - massive for British sport , brilliant , no doubt the@TeamGB effect has helped - #Rugby & #football must understand"
"Dunblane was known internationally for a terrible, horrible thing. Thanks to Andy Murray it's now known for something wonderful and amazing."
"Well deserved...Congratulations to the #USOPEN Champion Andy Murray!!!"
"Well done Andy Murray. Well done indeed. I hope you go and get plastered with Fergie and James Bond to celebrate."
"Get used to seeing @Andy_Murray winning Grand Slams... This is how it's going to be from now on!! Congratulations Andy 'The Machine' Murray"
"Congratulations Andy Murray for winning the U.S Open, top effort. #champion"
"Made up for @andymurray 1st major. Hopefully, thats the monkey off his back now and he can go on to win a lot more..."
"Massive congrats Andy Murray!!!! The first of many and well worth the wait!"