Joshua, 27, retained his unbeaten record in the most extreme of circumstances having been knocked to the canvas for the first time in his professional career. But he somehow found the strength to put 41-year-old Klitschko down in the 11th round in front of a euphoric post-World War II British record boxing crowd of 90 000 at Wembley.
In becoming the first pugilist to stop Klitschko since Lamon Brewster in 2004, Joshua added the WBA belt to his IBF and IBO titles.
The epic bout saw the world and his wife, from film stars to other top athletes, chip in with their congratulations.
The troubled former heavyweight champion Tyson Fury, who transformed the heavyweight scene when he became the first boxer in 11 years to defeat Klitschko in 2015, responded to Joshua's call for them to bring it on.
"Challenge accepted," tweeted Fury, who nevertheless has barriers to overcome in regaining his licence after being stripped of it over substance abuse and mental health issues which he says he is addressing.
"We will give the world the biggest fight in 500 years. I will play with you. You are a boxer's dream.
"Well done Anthony Joshua. Good fight. You had life and death with Klitschko and I played with the guy. Let's dance," added Fury, who has made derogatory jibes about Joshua calling him 'a poor man's Frank Bruno' among other things.
Hollywoood action hero, former Mr Universe and Governor of California Arnold Schwarzenegger expressed a hope that many had – of a rematch.
"One of the most exciting fights I've ever seen. Congrats @anthonyfjoshua on the win & @Klitschko on amazing battle. Hope there's a rematch," tweeted the 69-year-old Austrian-born star.
Bruno, who won his title at the third time of asking when he defeated Oliver McCall in 1995, said the bout had in an instant made heavyweight boxing the talk of the town after years of decline.
"The heavyweight division just got very exciting, the performance of both men 2night was incredible, whats next, looking 4ward 2 finding out," tweeted the 55-year-old whose reign lasted just one bout as he was defeated by American legend 'Iron' Mike Tyson.
Bruno and Joshua's compatriot and former heavyweight world champion Lennox Lewis – who never fought Wladimir but defeated his brother Vitali in what was to be the Briton's last bout – applauded both fighters for their performances.
"Crackin' Fight!!! Congrats to both for giving the fans something to talk about! Big up to AJ on the big win!!!" purred Lewis, like Joshua an Olympic champion but who won gold for adopted country Canada in 1988.
"How much heart did @Klitschko show in this fight? Gotta respect it. Hold ur head high brother! #joshuaklitschko."
Former WBC super middleweight champion Carl Froch, working as an analyst for Sky Sports, said Joshua had ticked all the boxes he needed to fill about his ability.
"There were a lot of questions – they've all been answered. Anthony Joshua came of age," Froch told Sky Sports.
"It was almost impossible what he did — but he did. He dethroned an old, admittedly, but still a king in Wladimir Klitschko.
"We’ve had a real treat this evening — it’s been unbelievable."
Britain's three-time Formula One world champion Lewis Hamilton took time out ahead of Sunday's Russian Grand Prix to tweet his own appreciation of the bout.
"Well done to both Anthony and Wladmir, but a huge congrats to @anthonyfjoshua for bringing it home! Great fight! #bigupyourself ====== =Y=Y=Y."
British athletics legend Mo Farah kept his tribute short.
"Legend," tweeted the quadruple Olympic champion.
The gallant Klitschko – who trailed on two of the judges scorecards – received lavish praise too.
"What a fantastic role model for all sports people @Klitschko is .... everyone can learn from the way he goes about his business ... #Respect," tweeted former England cricket captain Michael Vaughan.