The ace unified the heavyweight division twice in 22 fights.
And he is now aiming to become the undisputed champion next year.
Wilder and Fury face each other in an epic clash for the WBC world title in Los Angeles on December 1.
And the winner has been tipped to face Joshua immediately, with Wembley Stadium already booked for April 2019.
AJ holds the IBF, WBA and WBO belts, and admits he is hungry to add Wilder's WBC to his collection.
Joshua tweeted: "Unified the heavyweight division twice in 22 fights.
"Watch me become Undisputed Heavyweight Champion in 2019! Stay Hungry."
The 29-year-old Brit had been treating himself to a relaxing holiday in Jamaica.
But pictures from Instagram show Joshua is back in training at the gym, and he is clearly eager to get his next fight set up as soon as possible.
SHARE THIS STORY USING ANY OF THE BUTTON BELOW ⬇ PLACE YOUR TEXT ADVERT BELOW ⬇⬇⬇Unified the heavyweight division twice in 22 fights. Watch me become Undisputed Heavyweight Champion in 2019! Stay Hungry 🔥 pic.twitter.com/JTC99IfprO— Anthony Joshua (@anthonyfjoshua) November 21, 2018