Heavyweight boxing has moved closer to having an undisputed world champion: Joshua holds the WBA and IBF versions of the crown while Parker is the WBO champion and unbeaten in 24 contests, with 18 knockouts.
Joshua will put his World Boxing Association and International Boxing Federation belts on the line against Parker, the World Boxing Organisation champion.
Following weeks of negotiations, the 28-year-old Joshua confirmed the fight was on in a video posted on his official Twitter account.
Joshua's promoters, Matchroom Boxing, said the bout would take place at the 74,500-capacity Principality Stadium, best known for staging Wales rugby union internationals.
"It is a unification heavyweight championship fight. We all know what happened last time I was in a unification heavyweight championship fight -- it was gruelling, it was interesting and we both left the ring with masses of respect," the 28-year-old added.
"These fights aren't easy because there is a lot on the line, so respect to team Parker for taking the challenge. I am looking forward to it, training camp is under way and before you know it 31 March will be upon us."
Joshua, the London 2012 Olympic super-heavyweight champion, unified the WBA and IBF titles with a dramatic and hard-fought win over Wladimir Klitschko at Wembley in April before retaining both belts against Carlos Takam in a late-stoppage win in Cardiff in October.
Parker pushes punch power
Parker, 26, became the WBO champion in December 2016.
He made his British debut last year with a majority points win over challenger Hughie Fury, a cousin of former world heavyweight champion Tyson Fury.
Parker's performance against Fury did not impress some ringside observers.
But Parker was adamant his punching power would test Joshua.
"Anthony Joshua is in for a huge shock," he said. "A couple of months ago I heard him say 'Why should I be worried about this little kid from New Zealand?'
"Well, now he's about to find out. And the world is about to find out whether AJ can really take a punch. My entire existence is now devoted to proving what the boxing world already knows."
Sunday's announcement concluded weeks of sometimes fraught talks between the two camps.
"I'm delighted to get this fight made -- it's been a long time coming," said Joshua's promoter Eddie Hearn.
"Champions should fight champions and AJ continues to step up to the challenges."