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.
"Everything is on track. We've got a good structure and a good plan.
"Going into camp, everything is all good, everyone is happy. Just got to put in the work and prepare for March 31."
— Joseph Parker (@joeboxerparker) February 10, 2018
Photo Getty Images. Caption: Anthony Joshua and Joseph Parker