The 28-year-old from Sheffield, who became a father a week before the Masters and was subsequently the last man to arrive at Augusta, fired a final round of 67 to win by three shots.
It is Willett’s fifth win as a professional and will catapult him into the game’s elite.
Just nine years ago he was the Yorkshire Amateur champion.
He won as defending champion Jordan Spieth suffered an amazing collapse in the final round.
Spieth birdied four holes in a row from the sixth to reach the turn with a five-shot lead and seemingly certain to follow Jack Nicklaus, Nick Faldo and Tiger Woods in winning back-to-back titles at Augusta National.
However, the world No 2 – who had led for seven rounds in succession following his wire-to-wire victory last year – then dropped shots at the 10th and 11th and ran up a quadruple-bogey seven on the 12th after hitting two balls into Rae’s Creek in front of the green.
Willett, who was a doubt to even play the year’s first major before his wife Nicole gave birth to the couple’s first child the week before last, had birdied the 13th and 14th to reach the top of the leaderboard and another on the 16th helped point him towards a superb 67.
Dustin Johnson briefly closed within two of the lead with a birdie on the 15th, but double bogeyed the 17th to leave Spieth as the only man capable of preventing Willett from becoming the first English winner of the Masters since 1996 and the first European since 1999.
Birdies on the 13th and 15th kept Spieth’s hopes alive, but when he missed from eight feet for birdie on the 16th and bogeyed the 17th, Willett could celebrate a famous win.
“It’s awesome,” Willett said. “We played great golf today. It’s been a fantastic week. We had to go out and shoot a good score and put a little pressure on and luckily we have done that.”
Lee Westwood played the final round alongside his stablemate Willett and was within a shot of the lead when he chipped in for an eagle from the back of the 15th green.
However, the former world No 1 – who already held the record for the most top-three finishes (eight) in major championships without winning one – then three-putted the 16th and had to settle for a closing 69 and a share of second with Spieth.
“It’s a fine line between disaster and success and it happened to Jordan,” Westwood said. “Anything can happen at Augusta.”
England’s Paul Casey carded the lowest round of his Masters career, a 67, to achieve his best finish with a tie for fourth alongside Johnson and JB Holmes, with another Sheffielder Matt Fitzpatrick also shooting 67 to finish a shot further back with Soren Kjeldsen and Hideki Matsuyama.
“I played really well tee to green and gave myself lots of chances, that was the big thing,’’ said Fitzpatrick, 21, who missed the cut by a shot in 2014 after qualifying by winning the US Amateur title.
“I had a lot of putts between six and 15 feet and certainly on the back nine decided to hole them and that was the difference.”
Rory McIlroy, who went into the third round a shot off the lead but faded with a 77 on Saturday, carded a closing 71 but admitted he had felt the pressure of trying to win the Masters to complete the career grand slam.
“I was in a great position going into the weekend and I just didn’t play the golf I needed to when it really mattered,” said McIlroy, who finished joint 10th with Justin Rose, Daniel Berger, Brandt Snedeker and world No 1 Jason Day.
“That’s the thing that I take away not just from this week, but from previous Masters.
“I’ve been in position before and I haven’t got the job done when I needed to and I don’t think that’s anything to do with my game, I think that’s more me mentally – I’m trying to deal with the pressure of it and the thrill of the achievement if it were to happen. I think that’s the thing that’s really holding me back.”
Spieth, who has now finished second, first and second in his three Masters appearances, looked understandably emotional as he said: “It’s tough, really tough.
“Four birdies in a row and I knew that even par (on the back nine) is good by at least a shot and sometimes that makes it hard. You go away from the game plan and start playing conservative. A few weak swings and suddenly I am not leading any more.
“We still have the confidence that we are a closing team, we can close. I have no doubt about that ability. It was just a very tough 30 minutes for me that I hopefully never experience again.”