In what was billed as a clash of generations and perhaps the biggest heavyweight bout since Lennox Lewis beat Mike Tyson in 2002, the 27-year-old Joshua recovered from a knockdown in the sixth round to win one of the most thrilling fights in recent heavyweight history.
In doing so, the Englishman retained his IBF belt and gained the vacant WBA title, but the 41-year-old Klitschko pushed Joshua all the way.
Boxing great Sugar Ray Leonard tweeted: "Such an amazing fight with 2 great fighters. Lot of heart by both fighters. A lot of questions answered by @anthonyfjoshua #JoshuaKlitchsko."
Not since Len Harvey fought Jock McAvoy for the British light-heavyweight title at White City in 1939 had so many fans flocked to a boxing match in Britain, with 90,000 pouring through the turnstiles at the national stadium.
The fight was deemed so important that it was only the third in history, and the first staged outside of the US, to be broadcast on both American network rivals HBO and Showtime. It was also televised in 140 countries.
Those millions watching around the world tuned in to find out if Joshua might usher in a glorious new era for an ailing division, or if the Briton had bitten off more than he could chew against the former undisputed heavyweight king, a man who had contested 68 pro fights, 28 of them with world titles on the line.
Joshua, an Olympic champion in 2012, had been labelled "the saviour of heavyweight boxing" and was the clear favouite with British bookmakers.
But with only 18 professional fights to his name, and having never gone past seven rounds, the notion he would have an easy time of it against Klitschko was always questionable.
Klitschko turned pro after winning Olympic gold in 1996, when Joshua was only six years old, and first won a world heavyweight title in 2000.
His career hit the skids when he was knocked out twice in 2003 and 2004, but he won a world title again in 2006 and remained unbeaten until Tyson Fury dethroned him in 2015.
So insipid was the Ukrainian's display against Fury, many assumed age had caught up with him and he was a spent force.
But others suspected the humiliation of that defeat might inspire him to deliver one last bravura performance -- and so it proved in this epic bout.
Only Dillian Whyte had previously tested Joshua's chin, rocking his countryman when they met in 2015, and Klitschko, who had 53 knockouts before Saturday, did not waste any time posing questions of his own.
Rendered almost punchless by the awkward Fury, Klitschko found Joshua's jaw with a short overhand right in round two, while the champion struggled to find his range in the early stages.
Klitschko hurt Joshua with another right hand early in the fourth, before the champion fired back with a couple of his own.
The fight caught fire in the fifth, Joshua stunning Klitschko with a sharp right hand, wobbling him with a left before flooring him with a barrage of punches up close.
But a desperate Klitschko, now with a cut over his left eye, came charging back and Joshua looked to be out on his feet when the bell sounded.
The British fighter was floored by a huge right hand midway through the sixth -- the first time he had been put down in his pro career -- and Joshua did well to make it to his feet and even better to make it to the end of the round, having managed to evade more of Klitschko's wild swings.
Joshua's lack of head movement had allowed the challenger to open up a slight lead on the cards and Klitschko landed with two more juddering rights in the eighth and 10th, which Joshua did well to stand up to.
But Joshua went head-hunting in the 11th, flooring the challenger twice before referee David Fields called a halt to proceedings with Klitschko shipping blows on the ropes.
While this reporter had Klitschko ahead by two rounds when the end came, largely courtesy of his superior jab, the three ringside judges had it 96-93, 95-93 and 93-95 for Joshua.
Klitschko is now expected to retire after an illustrious career that will see him installed in the Hall of Fame one day, and his courageous efforts against a man 14 years his junior will have erased the embarrassment of defeat by Fury.
Joshua's future options include a unification match against undefeated American Deontay Wilder, the WBC champion who has 37 knockouts from 38 pro fights; or a unification match against New Zealand's WBO champion Joseph Parker, who was due to defend his title against Hughie Fury next month before the Briton pulled out with a back injury.
But the fight most fans want to see is Joshua against Hughie's cousin Tyson.
Fury's victory over Klitschko was seen as a passing of the heavyweight torch, but the Manchester fighter subsequently stumbled and dropped it.
Fury was stripped of the IBF belt for failing to defend against the mandated opponent and twice pulled out of scheduled rematches against Klitschko, before vacating the WBA and WBO belts, citing mental illness.
He is also without a boxing licence, having been stripped by the British Boxing Board of Control.
But the 28-year-old Fury, who believes he is the future of heavyweight boxing rather than Joshua, is back in training and hungry for a shot at his old titles.
For now, Joshua will take time to reflect on his achievement of beating Klitschko in only his 19th paid contest, while deciding how to spend his $19.4 million purse.
Meanwhile, fans will wonder if his might turn out to be the most exciting heavyweight reign since Tyson laid waste to all opposition during the 1980s.
One thing is certain: Joshua has breathed new life into boxing's blue riband division, which for over a decade was characterized by Klitschko's one-sided and often uninspiring victories over a succession of mediocre opponents.
Joshua's feats might also spark renewed interest in the US, where boxing has slipped from the public consciousness since Tyson's heyday.