The 28-year-old will look to defend his IBF, WBA and IBO belts against New Zealander Parker, who is making the third defence of his WBO strap which he won against Andy Ruiz in December 2016.
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.
But he is not expecting an easy night in the Welsh capital given that his 26-year-old opponent is undefeated in 24 fights and has won 18 of those via a stoppage.
Joshua said: "It is a unification Heavyweight championship fight, we all know what happened last time I was in a unification Heavyweight championship fight against Wladimir Klitschko last year.
"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. And you know me, I love this game. I am looking forward to it, training camp is underway and before you know it March 31 will be upon us."
Meanwhile, Parker is confident that he can stun Joshua and inflict a first defeat on the British boxer, who has won all 20 of his fights courtesy of a knockout.
He 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."