Joshua and Parker have agreed to put their IBF, WBA Super, IBO and WBO belts and unbeaten records on the line, ending a period of intense negotiation between the rival camps.
In his last outing, Joshua laboured to a tenth-round TKO win over tough late-replacement Carlos Takam, who had stepped in for the injured Kubrat Pulev, at the Principality Stadium in October.
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", Joshua said. I am looking forward to it.
"You never really can tell what sort of weight [Joshua is] going to be, but I know Joseph Parker will definitely be coming in a little lighter than he was for the Hughie Fury fight".
Talks had previously stalled over how the purse would be split but a compromise was reached last month which will see Parker, 25, earn 30-35%.
New Zealand's Parker (24-0, 18 KOs), 26, won a vacant title by majority decision over Andy Ruiz Jr.in December 2016 in New Zealand and has made two defenses.
CES 2018: Tech's biggest show disrupted by blackout
In the meantime, attendees had been evacuated from the affected space, which hosts booths for LG, Samsung and Sony among others. In a hilarious twist, the event lost power for nearly two hours, leading to some areas getting closed.
He said: "Anthony Joshua is in for a huge shock". A couple of months ago I heard him say "why should I be anxious about this little kid from New Zealand"?
"I've done it a few times now", he said.
The American, whose three-year reign as champion is the longest in the division, wants a fight with Joshua, calling the British Olympic gold medal victor out after beating Bermane Stiverne in November.
Joshua is strong favourite to come out on top given his performance in last April's 11th-round stoppage of former world champion Wladimir Klitschko at Wembley.
The victor of the clash is likely to face WBC champion Deontay Wilder in another unification bout this summer.
"Joseph Parker is the absolute epitome of the Kiwi sporting battler".
Wilder, 32, is 39-0 with 38 knockouts.