Williamson had missed the final two games against the West Indies last week due to a quad injury but is available for the September 6th-11th three-match series in Cairns.
Boult, who was released from his central contract with NZC at his own request earlier this month so he could spend less time travelling and more time at home with his family, is also in the 15-man squad.
"It's a great rivalry we have with Australia, it's always a huge occasion for the fans, and the team really look forward to it," Williamson said.
"You grow up watching the Chappell-Hadlee Trophy series and remembering the great battles, so to be part of another chapter is pretty special.
"We know how tough Australia are to beat in their own conditions and we're looking forward to the challenge."
Fast bowler Matt Henry has also recovered from a rib injury to be named in the squad at spinner Ish Sodhi's expense. Injuries to Kyle Jamieson (back) and Adam Milne (Achilles) meant they did not make the cut.
Australia, who have won the trophy six times, are the defending champions.
"We know how much the Chappell-Hadlee Trophy means to our fans and we're excited by the opportunity to head to Australia and try and win it back," coach Gary Stead said.
"With the ICC ODI World Cup in India just 14 months away - it's great to be playing more ODI cricket as we build towards the tournament next October-November."
NEW ZEALAND SQUAD
Kane Williamson (captain), Finn Allen, Trent Boult, Michael Bracewell, Devon Conway, Lockie Ferguson, Martin Guptill, Matt Henry, Tom Latham (wicketkeeper), Daryl Mitchell, Jimmy Neesham, Glenn Phillips, Mitchell Santner, Ben Sears, Tim Southee.
