The fight will see Joshua returning to the scene of his last fight where he took down Carlos Takam in what was his 20th professional win.
Joshua will defend his WBA, IBF and IBO belts in the fight, with Parker holding the WBO belt in what will be a massive unification bout.
"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.
"It's the first time in history that two reigning heavyweight World champions have met in Britain and it's a classic match-up between two young, fast, undefeated belt holders and it's going to be an explosive fight.
"This is another huge unification fight for Anthony as he continues to make history in the quest to become undisputed World heavyweight champion."
Parker's last fight was in England as he defended his WBO strap for the second time, outpointing Hughie Fury in Manchester in September, moving to 24-0 in the process.
The 26-year-old became New Zealand's first heavyweight world champion after landing the WBO belt in December 2016 against the undefeated Mexican American star Andy Ruiz in Auckland.
Parker's promoter David Higgins paid tribute to Hearn and Matchroom Boxing for the up-front way they had handled negotiations.
"Eddie has been great to work with from day one," Higgins said.
"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.
"New Zealand might be a tiny country on the other side of the world but it has a hugely proud sporting tradition – and a particularly strong tradition when it comes to whipping mother England.
"Joseph Parker is the absolute epitome of the Kiwi sporting battler. It has been said that he is punching above his weight, but he didn't become WBO heavyweight champion by being lucky.
"He's never been stopped, never even been wobbled in the ring. He's consistently fought fighters in the world's top ten and he's beaten them all easily. It certainly won't be a shock to me when he beats Anthony Joshua and takes his titles back home to New Zealand."
After lengthy negotiations, Parker is set to bank about $12million from the fight (not $30m as mentioned in some recent reports) – and even more in the rematch should he be successful.
A press conference featuring the main protagonists will soon be held in London.
