Parker will put his WBO strap on the line at the Principality Stadium, while Joshua's IBF and WBA belts will also be draped around the victor on March 31.
The pair will finally come together after months of negotiations between the representatives of both camps, the bout confirmed early in 2018.
Ahead of the fight Joshua said he hoped Parker would be fit enough to go the distance in their 12-round contest, and Parker has provided an update that should please the British boxer.
"Training has gone really good," he told Sky Sports News at his Las Vegas training camp.