The 43-year-old lefty saved his best for last as he came down the brutal back nine at the famed links course east of Edinburgh in 32, birdieing four of the last six holes, for a five-under 66.
That gave him a three under total of 281, three strokes clear of Henrik Stenson of Sweden, who had a closing 70.
Third place was shared by English pair Lee Westwood (75) and Ian Poulter (67) and Australian Adam Scott (72).
Mickelson won in what was his 20th Open campaign and it was his fifth major title after the Masters of 2004, 2006 and 2010 and the PGA Championship of 2005. It came just one month after he had endured the agony of a record sixth runner-up finish at the US Open behind Justin Rose.
“This is such an accomplishment because I never knew whether I’d be able to develop my game to play links golf. I played arguably the best round of my career, and shot the round of my life,” he said.
“The range of emotions I feel are as far apart as possible after losing the US Open. To win this feels amazing.
“You have to be resilient in this game. These last couple of weeks, these last couple of months, I’ve played some of the best golf of my career.”
Westwood, who started the day with a two stroke lead over the field, once again found himself coming up agonisingly short at a major tournament, the 62nd of his career.
“I didn’t really play well enough today. I didn’t play badly, but I didn’t play great. It’s a tough golf course, and you’ve got to have your “A” game,” he said.
“Phil obviously played well. He shot the round of the day, 5-under par, I think. And birdied four out of six (last holes). That’s a pretty special finishing in a major championship.”
Scott, who squandered a four shot lead with four to play at last year’s Open said: “I let a great chance slip.
“It’s a shame. But the game is there. I’m going to look forward to keeping it sharp next week and going to the World Golf Championship and another major in the next couple of weeks. I like where I’m at.”
Mickelson started the final round five strokes adrift of overnight leader Westwood, but held steady going out and then stormed down the back nine in a superb 32 at a time when all of his rivals were stumbling in the tough conditions.
It was the third straight Open won by a golfer in their 40s with Ernie Els and Darren Clarke both 42 when they won at Royal Lytham and Royal St George’s, respectively
Mickelson also became the first player in history to win the Scottish Open and then go on to win the British Open the following week.
Tiger Woods started the day tied for second, just two off the lead, but he failed to find any spark and his record of never having won a major when trailing after 54 holes held firm as he came in at two over 286 after a 74.
Throughout the day it was a bruising battle of wiles and wills among the the world’s best golfers with no quarter given and the mighty Muirfield links showing no mercy to the faint-hearted.
The lead changed hands at regular intervals, but in the end it was the experience and the expertise of the popular Mickelson that carried the day to secure the Claret Jug that goes to the winner of the British Open.
England’s Ryder Cup hero Ian Poulter set the early clubhouse target of one over 285 thanks to a magical putting display that saw him follow an eagle at nine with three straight birdies en route to a 67.
And with the sea breeze stiffening as the leaders worked their way around the turn and a cold mist drifting in from the Firth of Forth, he looked to be in good shape.
Scott had motored past Westwood to lead at two over at that stage with the Englishman one adrift alongside Stenson.
The Swede faltered at 12 and 13 and it was Mickelson who bounded up to near the top of the leaderboard.
Westwood then drifted away and back-to-back bogeys from Scott at 13 and 14 suddenly saw Mickelson with the lead.
He birdied the 17th to move two ahead and then had the 18th hole grandstand crowd on their feet as he sunk a 10-footer for birdie at the last.
That left Scott and Westwood needing a miracle to match him and neither looked likely of conjuring that up.
Mickelson had won The Open and the major tournament that had always been the hardest for him to compete in throughout his stellar career.