The 36-year-old American was claiming his second major title after a string of near misses and secured it by a five-stroke margin after a final round 68.
It left him at 20-under 268, beating the previous tournament best of 18-under set by both defending champion Tiger Woods, in 1997, and Jordan Spieth, in 2015.
He is the first top ranked golfer to win the Masters since Woods in 2002. And he has also beaten another Woods record by compiling his 11th straight round under par at Augusta.
Fifteen-time major champion Woods, who was in contention after a first round 68, achieved an unwelcome record of his own in round four, racking up a 7-over 10 at the treacherous short 12th -- the worst single hole score of his professional career.
Johnson, coming up behind, avoided the pitfall of Rae's Creek at that hole, which has ended the hopes of many contenders, and marched serenely on to his triumph with Sungjae Kim of South Korea and Australia's Cameron Smith in a tie for second at 15-under.
Woods presented Johnson the famous green jacket in the Butler Cabin, and Johnson admitted that he had been feeling the pressure going into the final round, despite his usual calm demeanor.
"I was nervous all day. I could feel it. The Masters to me is the biggest tournament, it's the one I wanted to win the most," he said. "I'm just very proud of the way I handled myself and the way I finished off the golf tournament."
"Honestly, it still feels like a dream," Johnson added. "As a kid, dreaming about winning and having Tiger put the green jacket on you, it still seems like it's a dream, but I'm here and what a great feeling it is and I couldn't be more excited."
Ahead by four shots overnight, Johnson was hot favorite to don the green jacket, despite being 0-4 in previous majors when leading before the final round.
But after a birdie on the third, the frontrunner offered a ray of light to his nearest challengers, Sungjae Im and Cameron Smith, with bogeys on the 4th and 5th, ending a run of 33 bogey-free holes.
Masters debutant Im birdied the 2nd and 3rd holes and closed to within a shot of Johnson at one point, but he could get no closer as he bogeyed the 6th and 7th, answered in part by a birdie on the 8th.
Record 20-under tally
Smith also hung tough with some spectacular recovery shots, but a hat trick of birdies for Johnson at the 13th, 14th and 15th gave him a comfortable cushion as he became the first player in Masters history to reach 20-under-par.
Johnson was able to par home for his 24th career PGA title, his four bogeys in the week the fewest of any Masters champion.
The 22-year-old Im, who was bidding to become the second Asian player to win a major, can take comfort from a solid last day performance as he carded a 69, while Smith can count himself unfortunate to be the first player in Masters history to shoot all four of his rounds in the 60s but still to come up short.
"That's cool," he said. "A lot of good around here this week."
Behind the leading trio, world number three Justin Thomas claimed 4th place on 12-under while Rory McIlroy finished tied 5th with Dylan Frittelli of South Africa a further shot back.
McIlroy, seeking the career Grand Slam, looked set to challenge with three birdies in his outward nine, but a bogey on the 10th halted his progress and he was once again unable to capitalize on the 13th and 15th par fives.
"I didn't have a great start but over the last 54 holes, only two bogeys, a lot of great golf in there," McIlroy said. "Not overthinking it as much could be the key for me."
Germany's Bernhard Langer, a two-time Masters champion, and at 63 the oldest player to make any Masters cut, fired a 71 to finish on 285.
Langer was one stroke ahead of US Open champion Bryson DeChambeau, who closed on 73, never quite getting to grips with the Augusta National course he had been set to overpower.
"I had some weird things happen to me I just couldn't foresee," DeChambeau said.
"I've got to fix this dizziness or whatever is going on. I've got to get healthy first and foremost."
DeChambeau and the world's other leading golfers will not have too long to wait for another chance of winning the Masters, with the famous major set to move back to its April slot next year after it was put back to November this year because of the global pandemic.