England face the Black Caps, who are one place ahead of them in the ICC Test rankings in fourth, in a day-night Test in Auckland from March 22-26 and then in Christchurch from March 30-April 3.
BBC Sport looks at why England can be considered favourites to win the series less than two years on from their miserable World Cup showing.
The matches will be played at five different venues.
Limited-overs skipper Eoin Morgan said: "Joe is good and should be fit to play tomorrow".
"Obviously the England team have had a tough Ashes, everyone knows that".
"The one-day side is very settled, with experienced individuals playing the way they want to play".
Meanwhile, Morgan confirmed that a decision on Alex Hales's return will be made on the morning of the first ODI in Melbourne.
"Everyone has been playing plenty of cricket so it won't be a case of England being rusty".
Fellow spinner Adil Rashid claimed three scalps, but England's quick brigade of Liam Plunkett (2-52), Mark Wood, Tom Curran and Chris Woakes all went at more than five an over after Victorian schoolboy Mackenzie Harvey unleashed with a 39-ball half-century.More news: NINE MASTS CAPITAL Ltd Takes Position in Twenty-First Century Fox, Inc
More news: Russian Federation will explain to United States sanctions against Iran, DPRK are vicious - diplomat
More news: CVS Health (CVS) Lifted to Overweight at Morgan Stanley
Wood, 27, was named in the squad for the first time since a year ago. During the same period, Australia reached 300 12 times in 50 matches, including 10 out of 23 matches batting first.
Steve Smith later said that while Australia's XI was yet to be settled, Warner should be fine to play.
A stomach bug continues to affect David Warner but the Australian vice-captain is expected to play in Sunday's one-day worldwide series opener against England. Dawid Malan has been called as a replacement of Stokes. So again there is the challenge of replacing two players.
Talking of allrounders, England will be hoping that the one-day series can help Moeen escape the funk the surrounded him for much of the Ashes.
Eoin Morgan has defended his head coach, Trevor Bayliss, before England's ODI series against Australia. I could have tried to play T20 cricket around the world, but I still don't see that as the strongest part of my game. "He signed a contract until 2019 and has always said the same thing".
"I get on really well with Glenn and it was good to catch up and have a chat".
Their only options, if they were to sack him, would be to do so at the end of this winter (to do so next summer would surely be a risk too far in respect of those World Cup aspirations) or else go down the split coaching route and have a separate head of the Test team, a path that the governing body are understood to be reluctant to take.
"That gave me a fair bit of confidence", he said.