Joshua's promoters Matchroom Boxing confirmed the deal on Sunday, concluding weeks of fractious negotiations between
the two sides.
Joshua will put his WBA and IBF titles on the line against New Zealander Parker, who has held the WBO version of the title since
Joshua said: "I would like to announce the official news that myself and Joseph Parker will be fighting on March 31 at Principality Stadium in Cardiff.
"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.
"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 March 31 will be upon us."
Joshua unified the WBA and IBF titles with his famous win over Wladimir Klitschko last April, before subsequently battling out a late stoppage win over Carlos Takam in Cardiff in October.
The 26-year-old Parker had made his UK debut one month previously, when he earned an underwhelming majority points
verdict over challenger Hughie Fury at the Manchester Arena.
Parker said: "Anthony Joshua is in for a huge shock. 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."