The bout was finally waved off by referee David Fields after Joshua's savage follow-up barrage following the round's second knockdown.
American Boxing legend Sugar Ray Leonard was among those who immediately hailed the contest as "amazing".
On the undercard is IBF featherweight champion Scott Quigg (35-1-2, 24 KOs) of Greater Manchester taking on Romanian Viorel Simion (21-1, 9 KOs). "A lot of questions answered by @anthonyfjoshua #JoshuaKlitchsko", he tweeted.
Round one: Both fighters come out jabbing, but Anthony Joshua lands the better flurries.
The veteran had even looked the more likely victor as he defied a 14-year age gap and was outboxing Joshua in the latter stages until the Briton produced a blistering finish to take his unbeaten record to 19 wins.
"I am not going to consider anything or be making any statements right now", he said.
Joshua, however, says he wants to fight Fury (25-0, 18 KOs).
"I'm not going to consider anything, I'm not going to make any statements, I will take my time and let you know", Klitschko said.
Fourteen years older than his opponent, he showed why he is one of boxing's most respected and enduring fighters but will go away with the refrain of "what if" ringing in his ears.
Ultimately, Joshua retained his already held IBF title, while winning the vacant WBA and IBO belts.
Joshua survived a knockdown for the first time in his professional career in the sixth round and looked close to surrendering his unbeaten record until his late bombardment forced the stoppage.More news: Samsung registers record profits in Q1 2017 despite decreased flagship mobile sales
"Two gentlemen fought each other". Anthony was better today.
"It was really good, I had fun".
And then there's Tyson Fury, the British nomad who upset Klitschko in 2015 before being waylaid by mental and other issues.
The Ukrainian had not fought since then and entered the ring as the underdog in front of Britain's largest boxing attendance since 1939.
Referring to Klitschko, Joshua continued, "He is a role model in and out for the ring and I've got huge respect and love for Wladimir Klitschko".
Wladamir Klitschko goes down against Anthony Joshua.
He also landed a fierce uppercut that sent the Ukranian wobbling on the ropes, and Joshua ensured there would be no comeback.
On a heady night, the most unaffected figure of all seemed to be Joshua himself.
Klitschko seized his moment and began to land flush as he took control of the unpredictable encounter.
It was a tale of two fights before the final round, with Joshua dominating early and knocking Klitschko down in the fifth.