The new world No. 3 overcame a one-stroke penalty awarded in bizarre fashion to secure a three-shot victory at Oakmont.
Johnson called an official while on the fifth green during his final round after his ball appeared to move. The 31-year-old insisted he hadn't caused the ball to move, which would've incurred a penalty, and playing partner Lee Westwood also absolved the American of any blame.
Leading the field, Johnson was informed on the 12th tee that a decision on the incident wouldn't be made until he had completed his round.
Although he was penalized, Johnson's lead over Ireland's Shane Lowry and compatriots Jim Furyk and Scott Piercy was such that it had no impact on the outcome of the tournament.
"I just tried to focus on each shot, not worry about what had happened," Johnson told CNN. "Whether I got the penalty or not, ultimately it didn't matter."
Johnson's win, which came at his 29th career major, was warmly received by fellow pros Jordan Spieth and Rory McIlroy -- who both tweeted their congratulations.
"To finally put it all together on a Sunday and get that first major championship is absolutely huge," added Johnson, who has suffered heartbreak at golf's biggest events in the past.
In 2010, Johnson missed out on a place in a playoff at the U.S. PGA Championship as a result of a penalty.
He also led the field at the halfway point of last year's British Open, only to fall away over the weekend.
"It's a huge monkey off my back. Especially with all the near misses I've had in a lot of majors in the last few years," he said.
"This one is definitely going to be special in my heart forever."