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Two-time world heavyweight champion Joshua will attempt to get his career back on track with a victory over Franklin in his homeland following back-to-back defeats to Oleksandr Usyk.
Usyk claimed the WBA, IBF and WBO belts by beating the Briton in September 2021 and retained them with victory in the rematch in Jeddah last August.
Franklin was beaten by Dillian White in his last fight last November, that being the American's only defeat in 22 professional bouts.
Joshua is eager to impress his new head trainer Derrick James in what will be his first fight at The O2 since 2016.
"I'm looking forward to stepping back into the ring on April 1 at The O2 in London," said the 33-year-old Joshua. "Mentally and physically I feel ready.
"I want to put on a show and impress my coach as he has high standards. Franklin has a good style and a great attitude, which he has shown in recent fights."
Eddie Hearn, Joshua's promoter, last week stated that he expects the 2012 Olympic champion to make a statement when he faces Franklin but knows "we've got a major problem" if he is beaten again.
Franklin warned he will inflict more pain on Joshua in his homeland.
"I'm ready to show the world why it's time for me to take my place at the top of the heavyweight division," said Franklin.
"Joshua had his time. It's my time to shock the world. This fight isn't going to the judge's card. I will have win number 22 come April 1. That ain't no April Fool's joke."