The 29-year-old will fight away from the UK for the first time as he looks to take a bite out of 'The Big Apple' at New York's Madison Square Garden.
AJ had Wembley Stadium booked for April 13 as he chased a bout against Deontay Wilder, but the American has been ordered by the WBC to face Tyson Fury in a rematch.
Joshua will be a heavy favourite against the Brooklyn brawler, who has racked up 23 wins out of 24 fights, with 20 victories coming by way of knockout.
Addressing the fight to fans, the Olympics gold medallist said: "I’m going to be defending my heavyweight titles at MSG aka Madison Square Gardens against a fighter named Jarrell Miller aka Big Baby Miller.
"You know the state of the heavyweight division is full of boxing politics but you know how it goes I’ve just got to roll with the punches."
While on his YouTube channel, he added: "The time has come to head across the Atlantic and defend my heavyweight titles in the USA.
"I am looking forward to taking on another challenge with a good boxer and a brilliant talker.
"It will be an exciting fight, I will leave nothing to chance, and plan on dismantling Miller in style to make my mark."
While Miller is adamant he will shock the world in the summer, as he branded his rival as a "punk".
He said: "AJ is making a huge mistake coming over here to fight me in my own backyard.
"He wants to announce himself on the American stage, but all he's doing is delivering me those belts by hand. It's dog eat dog in the ring and this dog has got a bigger bite. He'll be leaving New York empty-handed.
"This is the fight that I've been chasing all my life. On June 1, I'm going to achieve the thing I was born to do and win the heavyweight championship of the world.
"That punk AJ is standing in the way of my dreams and on June 1 he's getting run the hell over."
Dillian Whyte had been mooted as a possible option to face Joshua after his stunning KO win against Dereck Chisora, but he is now set to face former world title challenger Dominic Breazeale.
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