Australia's National Selection Panel (NSP), under the chairmanship of Andrew Hilditch met on Tuesday to pick the squad, to be led by Ricky Ponting.
Clarke earlier cited "personal reasons" for quitting midway through the ongoing ODI series and left the team hotel on Monday.
All-rounder Ryan Harris, who has recovered from an injury also returned to the Test squad, which also has left-hand opening batsman Phillip Hughes, a Cricket Australia release said.
Meanwhile, young all-rounder Steven Smith got the reward of his impressive performance in Australian domestic circuit as the 20-year-old was also included into the squad.
"The core of the squad is the Australian Test team that performed so well during the Australian summer in defeating West Indies and Pakistan," Hilditch said.
"Ryan Harris, having overcome injuries at the start of the season, has played really well for Australia in the shorter formats of the game. The NSP are confident that if Ryan gets an opportunity he has the ability to have an impact for Australia in what will be a very hard Test series against New Zealand.
"Phillip Hughes has also been in excellent form at state level and richly deserves his selection on the back of another fantastic season in the Weet-Bix Sheffield Shield," Hilditch said.
"Steven Smith has had an excellent Shield season, including a big century against Tasmania recently, and of course has already demonstrated his ability to cope with the pressure of international cricket.
He adds great flexibility to the squad with his exciting stroke-play, leg-spin bowling and gifted fielding," the chief selector added.
Wellington will host the first Test and the second one will be held at Hamilton from March 27.
Squad: Ricky Ponting (capt), Michael Clarke, Doug Bollinger, Brad Haddin, Nathan Hauritz, Ryan Harris, Phillip Hughes, Mike Hussey, Mitchell Johnson, Simon Katich, Clint McKay, Marcus North, Steven Smith, Shane Watson.