Joshua holds the WBA and IBF versions of the crown while Parker is the WBO champion and unbeaten in 24 contests, with 18 knockouts.
Following weeks of negotiations, the 28-year-old Joshua confirmed the fight was on in a video posted on his official Twitter account.
“These fights aren’t easy because there’s a lot on the line so respect to team Parker for taking the challenge. And you know me, I love this game,” he said.
“I‘m looking forward to it, training camp is under way and before you know it, March 31st will be upon us.”
The winner of the fight will take a step towards becoming the first undisputed heavyweight champion since Lennox Lewis in 1999.
American Deontay Wilder holds the fourth belt in the heavyweight division.
Reporting by Shrivathsa Sridhar; Editing by Toby Davis