ST ANDREWS, 20 Jul 2015 (AFP) - It was the 39-year-old American's second major title win after he triumphed at the 2007 Masters.
"It sounds beautiful. It still sounds extremely surreal. The tone to it is very humbling. I feel blessed to be the champion and honoured to be part of the history of this game," Johnson said.
Jordan Spieth, meanwhile, missed getting into the playoff by one shot and thus saw his hopes shattered of becoming just the second player to win the Masters, US and British Opens in the same year
Johnson, Oosthuizen and Leishman all finished with totals of 15-under 273 after Johnson and Leishman had 66s and Oosthuizen a 69.
That forced the first British Open playoff since Stewart Cink defeated Tom Watson at Turnberry in 2009 and the first three-way playoff since 1999 when Paul Lawrie triumphed.
It was a gripping end to what had been an enthralling day that saw a packed leaderboard go hammer and tongs at grabbing enough birdies to take possession of golf's most coveted trophy on just the second occasion in it's 155-year-long history when it concluded on a Monday.
Torrential rain on Friday and high winds on Saturday had seen to that.
Played over holes 1, 2, 17 and 18, Oosthuizen and Johnson immediately distanced themselves from Leishman with opening birdies to his bogey.
Johnson then went clear with a birdie at the second, but he hit a poor approach to the notorious 17th, the Road Hole, and bogeyed, only for Oosthuizen to miss a four-footer to get back on level terms.
It all came down to the famous 18th hole with its historic town centre backdrop, and a par was enough for Johnson with Oosthuizen narrowly missing an eight-footer to force sudden death.
"To don my name on that trophy is humbling and surreal," said Johnson, whose superb wedge-play and putting were key to his win.
"It has been a week of patience, courage and trust. I can't play any better than I did. I just stayed in it, waited for the opportunities and made a few putts.
"I don't like seeing it end on a miss. Louis is a buddy, a friend and a tremendous competitor."
Oosthuizen, who was looking to make it back-to-back Open wins at St Andrews having triumphed at the Old Course by seven strokes in 2010, said that he had done well just to get into the playoff.
It was the second time he had lost a major in a playoff after losing to Bubba Watson for the 2012 Masters green jacket.
"But I'll take a lot out of this week," he said.
"I was really motivated to win this championship this week. I love this place, I've said it a thousand times. I can't wait for it to come back here again," added the 32-year-old, who finished tied for runner-up as well in this year's US Open behind Spieth.
The playoff followed a sensational day of aggressive shot-making under the drenching Scottish rain when it soon became clear from the nature of the early scores that the Open crown would go to the lowest of the low.
The three-way overnight lead held by Oosthuizen, Justin Day and Irish amateur Paul Dunne was immediately shattered when the understandably nervy Irishman bogeyed the first two holes from which he never recovered.
Johnson and Adam Scott came charging out of the pack as the rain showers came and went, but the packed leaderboard was as fickle as the weather, and predicting who would emerge triumphant at the end of the day was nigh-on impossible.
Spieth was well in the hunt, but a double-bogey at the par-three eighth had him chucking his ball away in anger.
Others fell away too as they failed to keep up in the unrelenting birdie stakes and it all came down to a dogfight down the back nine with the punishing six last holes holding the key to victory.
Leishman pushed his nose in front with six holes of his round to play and he made a drive for glory only to lose his outright lead by missing a four-footer at the 16th.
Johnson sunk a snaking, downhill 20-footer for birdie at the last to get to 15 under and it was up to Leishman, Spieth, Day and Oosthuizen coming up behind him to match or better his score.
Spieth came to grief with a bogey at the 17th as his Triple Crown dream died, but Leishman held firm at 15 under and they were joined in the playoff by Oosthuizen, who sunk a six-footer at the last for a birdie.
Collated final scores and totals in The 144th Open Championship at St Andrews on Monday (Gbr & Irl unless stated, par 72) ((a) denotes amateur):
273 - Zach Johnson (USA) 66 71 70 66, Marc Leishman (AUS) 70 73 64 66, Louis Oosthuizen (RSA) 67 70 67 69
Zach Johnson won the four hole Playoff with a score of -1
274 - Jason Day (AUS) 66 71 67 70, Jordan Spieth (USA) 67 72 66 69
277 - Justin Rose 71 68 68 70, Sergio Garcia (ESP) 70 69 68 70, Danny Willett 66 69 72 70, Jordan Niebrugge (a) (USA) 67 73 67 70
278 - Adam Scott (AUS) 70 67 70 71, Brooks Koepka (USA) 71 70 69 68
279 - Anthony Wall 70 71 68 70, Oliver Schniederjans (a) (USA) 70 72 70 67, Brendon Todd (USA) 71 73 69 66, Ashley Chesters (a) 71 72 67 69, Martin Kaymer (GER) 71 70 70 68, Luke Donald 68 70 73 68, 280 Hideki Matsuyama (JPN) 72 66 71 71, Robert Streb (USA) 66 71 70 73
281 - Retief Goosen (RSA) 66 72 69 74, Greg Owen 68 73 71 69, Branden Grace (RSA) 69 72 73 67, Stewart Cink (USA) 70 71 68 72, James Morrison 71 71 70 69, Phil Mickelson (USA) 70 72 70 69, Russell Henley (USA) 74 66 72 69, Padraig Harrington 72 69 65 75, Marcus Fraser (AUS) 74 69 68 70, Patrick Reed (USA) 72 70 67 72
282 - Matt Jones (AUS) 68 73 69 72, Ryan Palmer (USA) 71 71 67 73, Steven Bowditch (AUS) 70 69 69 74, Andy Sullivan 72 71 68 71, Jim Furyk (USA) 73 71 66 72, Paul Dunne (a) 69 69 66 78, Jimmy Walker (USA) 72 68 71 71, Billy Horschel (USA) 73 71 71 67, Rickie Fowler (USA) 72 71 66 73, Anirban Lahiri (IND) 69 70 71 72
283 - Francesco Molinari (ITA) 72 71 73 67, John Senden (AUS) 72 72 68 71, Scott Arnold (AUS) 71 73 73 66, Geoff Ogilvy (AUS) 71 68 72 72, Webb Simpson (USA) 70 70 71 72, Marc Warren 68 69 72 74, Paul Lawrie 66 70 74 73, Rafael Cabrera-Bello (ESP) 71 73 68 71, Henrik Stenson (SWE) 73 70 71 69
284 - Graeme McDowell 72 72 70 70, David Howell 68 73 73 70, Ryan Fox (NZL) 72 69 76 67, David Duval (USA) 72 72 67 73, Hunter Mahan (USA) 72 72 67 73, Dustin Johnson (USA) 65 69 75 75, Jamie Donaldson 72 71 71 70, Eddie Pepperell 72 70 66 76, Lee Westwood 71 73 69 71
285 - Kevin Na (USA) 67 75 70 73, Jason Dufner (USA) 73 71 67 74, Greg Chalmers (AUS) 70 71 69 75, David Lipsky (USA) 73 69 70 73, Gary Woodland (USA) 72 70 71 72, Matt Kuchar (USA) 71 73 70 71, Cameron Tringale (USA) 71 71 73 70
286 - Ernie Els (RSA) 71 73 69 73, Romain Langasque (a) (FRA) 69 72 71 74, Thongchai Jaidee (THA) 72 71 70 73
287 - Richie Ramsay 72 71 70 74, Charl Schwartzel (RSA) 67 72 69 79, Ross Fisher 71 73 72 71, Graham Delaet (CAN) 71 73 68 75, Bernd Wiesberger (AUT) 72 72 71 72, Harris English (USA) 71 72 69 75
288 - Ben Martin (USA) 74 70 67 77, Brett Rumford (AUS) 71 71 71 75, Paul Casey 70 71 75 72, David Lingmerth (SWE) 69 72 70 77
289 - Bernhard Langer (GER) 74 70 73 72, Mark O'Meara (USA) 72 72 71 74
290 - Thomas Aiken (RSA) 75 69 72 74