Joshua will put his World Boxing Association and International Boxing Federation belts on the line against Parker, the World Boxing Organisation champion.
Speaking about the bout, Joshua said via a Matchroom statement: "It's a unification heavyweight championship fight, everyone knows what happened the last time I was in one".
He said: "I' like to wish you all a happy new year". "Training camp is underway and before you know it, March 31 will be upon us".
Parker, 24, has won all his 24 pro fights, winning 18 by stoppage.
Joshua suggests that Parker does not deserve to be mentioned alongside other champion sportsmen and will not offer a gesture of appreciation after he delivers a first humbling loss to the 26-year-old. "A couple of months ago I heard him say "why should I be anxious about this little kid from New Zealand"?"
"Well, now he's about to find out".
After 20 straight victories, all by knockout, Joshua hopes to take another step towards becoming the undisputed world heavyweight champion. My entire existence is now devoted to proving what the boxing world already knows'.More news: Cuba condemns Trump's "racist" statements on Haiti, El Salvador
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Negotiations have been taking place between the two camps for several months, with Parker's representative, David Higgins flying to the United Kingdom last week to finalise the deal.
"I haven't seen them all, but I've heard some of them", Joshua said when asked about the provocative comments coming from Parker which continued in mainstream British media over the weekend. "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".
"Joseph Parker is the absolute epitome of the Kiwi sporting battler".
Joshua became IBF heavyweight champion by defeating Charles Martin at London's O2 Arena in April 2016.
"He's never been stopped, never even been wobbled in the ring. It certainly won't be a shock to me when he beats Anthony Joshua and takes his titles back home to New Zealand". 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.
March is set to be a huge month for heavyweight boxing, as unbeaten American Deontay Wilder (39-0) is also set to defend the WBC heavyweight strap against Cuba's Luis Ortiz (28-0) at the Barclays Center in Brooklyn on the 3rd.