Grand slam-chasing Jordan Spieth needed a birdie on the 18th hole at St Andrews to join the four-hole aggregate play-off, but saw his approach spin back off the green into the Valley of Sin and narrowly missed the birdie attempt.
Johnson had set the clubhouse target on 15 under after a closing 66 that was matched 40 minutes later by Leishman, whose total of 130 for the third and fourth rounds – he carded a flawless 64 on Sunday – equalled the lowest 36-hole total in major history.
Oosthuizen, who won the 2010 Open at St Andrews, still had two holes to play and after a crucial par save on the 17th the South African birdied the 18th from five feet to make it a three-way aggregate play-off on the first, second, 17th and 18th.
Johnson and Oosthuizen both birdied the first as Leishman three-putted from long range and Johnson edged ahead with another birdie on the second.
All three players bogeyed the 17th and after Johnson missed his birdie attempt on the 18th, Oosthuizen’s attempt from 12 feet also missed to give Johnson his second major title, eight years after victory in the Masters.
An emotional Johnson said: “I feel blessed to be the champion, I feel honoured to part of the history of this game and to don my name on that trophy, especially with the names before me. Humbling and surreal are two words that come to mind.
“I can’t play any better than what I did. I had a lull on Friday and Saturday, but nothing significant, but stayed in it and waited for the opportunities and made a few.”