Joshua, 28, holds the IBF and WBA belts, while New Zealander Parker is the WBO champion.
In his last fight inside the Principality Stadium in October, Joshua claimed a 10th-round stoppage victory over Cameroonian-born French boxer Carlos Takam.
Parker's camp had been desperate to hold a unification match-up with Joshua and held a press conference last November where they showed video footage of the Briton being floored during his time as an amateur.
'These fights aren't easy because there is a lot on the line, so respect to team Parker for taking the challenge.
It's obvious that Barry does not want Parker to stand right in front of Joshua, and will likely have his fighter on the move while looking to counter Joshua - who is usually a come forward puncher with plenty of aggression. Then Parker flew there this weekend with the deal all but done for a fight that will be televised on Sky Sports Box Office pay-per-view in the United Kingdom.
A few days ago, trainer Rob McCracken discussed his plan to ensure that his star fighter, Anthony Joshua (20-0, 20 KOs), would be lighter for his next contest. "A couple of months ago I heard him say 'why should I be anxious about this little kid from New Zealand"? "Champions should fight champions and AJ continues to step up to the challenges".
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"I'm delighted to get this fight made - it's been a long time coming", Hearn. "Being involved in a big fight is exciting - it's going to be a little part of history".
The victor of the clash is likely to face WBC champion Deontay Wilder in another unification bout this summer.
The division's other undefeated champion, World Boxing Council belt holder Deontay Wilder, defends his crown against Cuba's Luis Ortiz at the Barclays Centre in Brooklyn, New York, on March 3, it was announced earlier in the day.
"Joseph Parker is the absolute epitome of the Kiwi sporting battler".
Parker (24-0) picked up the vacant WBO title with a points win over the previously unbeaten Andy Ruiz Jr.in Auckland in December of 2016. He's consistently fought fighters in the world's top ten and he's beaten them all easily.
Wilder, 32, is 39-0 with 38 knockouts.
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