Johnson recovered from a somewhat shaky start to card a final round of 68 and win his second major title by five shots from Australia's Cameron Smith and South Korea's Sungjae Im.
The world number one's winning total of 20 under par set a new tournament record, beating the previous best of 18 under set by Tiger Woods in 1997 and equalled by Jordan Spieth in 2015.
And as the defending champion, Woods was on hand to present Johnson with his green jacket in the traditional ceremony in the Butler Cabin.
"Always around the putting green growing up, it was putts to win the Masters," Johnson said. "It was always to win at Augusta, especially because I grew up so close to here, about an hour, hour and 10 minutes away.
"As a kid you dream of playing in the Masters and dream about putting on a green jacket. Still kind of think it's a dream, but hopefully it's not.
"Obviously having Tiger put it on was awesome and unbelievable and you wouldn't want it any other way. But any guy could put it on me and I'd be just fine!"
Johnson took a four-shot lead into the final round but saw that reduced to a single stroke after playing the first five holes in one over par while Smith and Im picked up two early birdies.
However, he responded well to birdie the sixth and eighth and a hat-trick of birdies from the 13th sealed a commanding victory to go with his 2016 US Open success.
"It's always tough to get it done in a major," added Johnson, who had failed to convert any of his four previous 54-hole leads into major victories.
"No matter how good you're playing it's hard. 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. I'm just very proud of the way I handled myself and the way I finished off the golf tournament."
Johnson shared the triumph with his brother and caddie Austin, adding: "It's an unbelievable feeling to experience all this with my brother.
"He's been a big help being on my bag. I love him being on my bag and I wouldn't want anyone else there. To share all these memories and moments with him is incredible.
"I had to jab him a little on 18 because he was tearing up, made me tear up. I've still got to finish this off, I can't be crying. It was a lot of fun, I will remember this for the rest of my life."
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