It is the first time back at Wembley since that Klitschko bout, and the 28-year-old has revealed he thinks tonight will be his second-toughest match since the Ukrainian.
Joshua and his opponent from New Zealand went into this fight unbeaten, but the British overcame Parker who has never been down according to the commentator of the fight.
Joshua put on a dazzling performance on Saturday night as he emphatically knocked out mandatory challenger Alexander Povetkin in round seven. Knocking the Russian initially, Povetkin made it up within the count, but not for too long.
Heavyweight world titleholder Deontay Wilder and former world champion Tyson Fury finalized their deal Friday night, and Premier Boxing Champions announced the fight would take place December 1.
LONDON, ENGLAND - SEPTEMBER 22: Anthony Joshua celebrates victory over Alexander Povetkin during the IBF, WBA Super, WBO & IBO World Heavyweight Championship title fight between Anthony Joshua and Alexander Povetkin at Wembley Stadium on September 22, 2018 in London, England.
Wilder said in a video posted to his Instagram account that he just defeated one of the best heavyweights in the world in Luis Ortiz earlier this year and that he's now coming for the next best fighter in the division. When I fought Klitschko, I was much weaker and in worse shape than I am now. "Every jab takes a breath out of you and I slowed him down".
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Former heavyweight world title challenge Scott Welch has no doubts that Joshua is now on the way to becoming the world's richest sportsman.
But the first round ended with Povetkin, stooping low, rocking Joshua with a right uppercut that drew blood from the champion's nose.
"Without that Klitschko fight - I wasn't as prepared as I am now".
'Wilder is my number one choice but I am done talking now'.
After struggling in the first two rounds, Joshua took control of the fight in the third, and as the rounds wore on it became increasingly clear that there was only going to be one victor.
Joshua says he will fight someone on 13 April and "give the fans what they want" but he won't say who it might be.