Breazeale, 30, has won all 17 of his professional fights, with 15 knockouts.
Joshua, 26, won the title with a second-round stoppage of American Charles Martin on 10 April.
"I am looking to get past Breazeale in style and continue moving towards the unification fight everybody is waiting for," said undefeated Joshua.
Breazeale, who is an inch taller than Joshua at 6ft 7in, is a former Olympian and ranked 13th in the IBF rankings, below British pair Dereck Chisora and David Haye.
Media playback is not supported on this device
Londoner Joshua, the 2012 Olympic super-heavyweight gold medallist, added: "It's sure to be explosive, both of us like to let our hands go and score knockouts."
British super-middleweights George Groves and Martin Murray will meet on the undercard in an eliminator bout for the WBA crown.
Joshua's promoter Eddie Hearn had said his fighter's next bout was due to take place on 9 July at Wembley, but the plan was changed when Tyson Fury - the WBA, IBO and WBO heavyweight champion - announced his rematch with Wladimir Klitschko would take place on the same date in Manchester.
IBF heavyweight world champion Anthony Joshua will make the first defence of his title on 25 June against American Dominic Breazeale at London's O2 Arena.