"AJ is one of the strongest in the division, I'm happy to have this opportunity and we will give the fans a good fight".
"My number one would be Wilder, let's not talk about a number two or three", Joshua said, although the British fighter then added that if Dillian Whyte wanted to fight he is "also more than welcome".
Anthony Joshua delivers the knockout blow on Alexander Povetkin.
Povetkin's defeat by Klitschko came on the same night Joshua made his professional debut by stopping the little-known Emanuele Leo at the 02 Arena, when even for all of the excitement surrounding Joshua, it was Klitschko-Povetkin that demanded the greatest attention.
United Kingdom rapper Nines, meanwhile, performed a spin of his song "I see you shining" as the intro for Joshua to come out for his ring walk.
Joshua's next fight will take place on April. 13, again at Wembley Stadium, and an opponent is yet to be announced.
"We've already tried once - we signed a contract, they didn't - and now he's fighting [former unified world champion Tyson] Fury".
Povetkin got up but was sensibly stopped as Joshua pummelled him with punches in front of a crowd close to 80,0000 at Wembley Stadium.
Joshua, 28, had a significant height and reach advantage of several inches over Povetkin.
Povetkin, 39, knew this was most likely his last shot after being floored four times in a unanimous points loss to Wladimir Klitschko five years ago. After sending the Russian to the canvas with a left-right combination after hurting him with a big right hand, the referee Steve Gray intervened to rescue Povetkin once he was back on his feet and unable to defend himself from another hurtful barrage of punches.
Both men had won Olympic gold medals, but it was the youthful energy of the 28-year-old Joshua which proved decisive as Povetkin visibly exhausted halfway through the contest.