Fury has signed a promotional deal with Frank Warren which will bring him under the BT Sport boxing umbrella.
Fury also suggested Joshua, who now holds the WBA, WBO, IBF and IBO championship belts, is now second fiddle to American WBC king Deontay Wilder in the division.
Fury (25-0, 18 KOs) held a news conference Thursday to announce he will headline a card on June 9 at the Manchester Arena in his native England against an opponent to be determined. "Most people can relate to what I've gone through".
That would see WBA, WBO and IBF champion Joshua entering the ring against WBC heavyweight title holder Wilder first, with Fury enjoying a couple of warm-up fights before taking on the victor of that grudge match later in the year - New Year's Eve fights are always big business in boxing, after all.
Joshua-Wilder would take place either at Wembley Stadium in London or the Principality Stadium in Cardiff, with the possibility of a rematch next year in the United States.
The pair will once again work together following a brief yet successful relationship in 2014, which saw Fury secure his mandatory position to challenge Wladimir Klitschko by defeating Dereck Chisora in November of 2014.
"I can't wait to get in there and prove I am the best, even after all this time out", said Fury.
"I'm the fittest I've ever been. The reflexes are as good as they've ever been".
"Wilder is top of the tree - he's unsafe until the last two seconds of the fight", he added.
Fury added: "The fans have been showing me a lot of love of late".
While Fury's decision indicates a long-awaited bout between the two remains but a pipe dream for now, the Gypsy King's temperament would suggest that he won't stop until he gets the fight he wants.
Tyson Fury odds: Who could he fight next?
Joshua should face Deontay Wilder next as he tries to become the undisputed champion, but if they fail to agree a deal he will fight Russian Alexander Povetkin.
Former heavyweight boxing champ Tyson Fury explains how the "mac is back" to reclaim the world.