Joshua posted a video on Twitter confirming the fight for Cardiff as he bids to unify the belts in the heavyweight division.
Parker himself is looking to extend his own undefeated streak, with the WBO Heavyweight champion now 24-0 in his professional career, coming off a successful defence of his Heavyweight championship against Hughie Fury at Manchester Arena in September.
"Anthony Joshua is in for a huge shock", Parker said.
Joshua's promoters Matchroom Boxing confirmed the deal on Sunday, concluding weeks of fractious negotiations between the two sides. The 26-year-old became New Zealand's first heavyweight world champion when he landed the WBO strap in December 2016 against the undefeated Mexican American star Andy Ruiz in Auckland.
GETTY IMAGES Joseph Parker's pre-fight approach has Anthony Joshua riled
The WBA, IBF, WBO and IBO World titles will be on the line on Easter weekend, in the same stadium where Joshua extended his undefeated record to 20-0, with a tenth round TKO victory over Carlos Takam, in October. "A couple of months ago I heard him say 'why should I be anxious about this little kid from New Zealand"? And the world is about to find out whether AJ can really take a punch. "I know we ruffled a few feathers along the way but, as Eddie acknowledged, when you come from a small country and people perceive you as a small player, sometimes you've got to make a bit of noise".
"He's never been stopped, never even been wobbled in the ring. It certainly won't be a shock to me when he beats Anthony Joshua and takes his titles back home to New Zealand".
"I would like to announce the official news that myself and Joseph Parker will be fighting on March 31 at Principality Stadium in Cardiff", Joshua is quoted by The Telegraph as saying.
An announcement on ticket prices and sale dates will be made soon.