Joshua had hoped for a rematch against Klitschko later this year, likely in Las Vegas, but the Ukrainian recently announced that he has now retired from the sport for good.
Pulev was then made the favourite to be Joshua's next opponent, with Cardiff mooted as the host city, and it has now been set in stone for seven weeks' time.
Writing on his personal Facebook page, Pulev started the war of words by saying: "Anthony Joshua is a great and dangerous rival, but his style fits perfectly with mine. In boxing, the boxers' styles dictate the match and there'll be not many hugs, there will be a heavy boxing."
Pulev has suffered just one defeat in 26 fights, losing to Klitschko in Hamburg three years ago on a fifth-round knockout.