England's Tim Bresnan out of New Zealand tour
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"We discussed it with him and felt the best way forward was for him to go back to Somerset, work on his game and get a lot of runs early in the season."
Root has made his debut in all three international formats in India, with the Yorkshireman helping Alastair Cook's men clinch a 2-1 series win in the drawn fourth Test in Nagpur last month.
"He's already shown us what he can do and he's shown he is very, very easy in the international arena," Miller said. "We're excited about him."
Spinner Samit Patel and middle-order batsman Eoin Morgan were both dropped from the Test squad.
England last played a Test series in New Zealand in 2008, winning the three-match contest 2-1.
A Twenty20 side led by Stuart Broad start a three-match series in Auckland on February 9, with the first ODI in Hamilton on Feb 17.
The first of three Tests is due to start in Dunedin on March 6.
England squads for New Zealand:
Test squad: Alastair Cook (capt), James Anderson, Jonathan Bairstow, Ian Bell, Stuart Broad, Steven Finn, Graham Onions, Monty Panesar, Kevin Pietersen, Matt Prior (wkt), Joe Root, Graeme Swann, Jonathan Trott, Chris Woakes.
Twenty20 squad: Stuart Broad (capt), Jonathan Bairstow (wkt), Danny Briggs, Jos Buttler (wkt), Jade Dernbach, Steven Finn, Alex Hales, Michael Lumb, Stuart Meaker, Eoin Morgan, Samit Patel, James Tredwell, Woakes, Luke Wright.
ODI squad: Alastair Cook (capt), James Anderson, Jonathan Bairstow (wkt), Ian Bell, Stuart Broad, Jos Buttler (wkt), Steven Finn, James Harris, Eoin Morgan, Samit Patel, Joe Root, Graeme Swann, James Tredwell, Jonathan Trott, Chris Woakes
Twenty20 series: Feb 09: 1st Twenty20, Eden Park, Auckland; Feb 12: 2nd Twenty20, Seddon Park, Hamilton; Feb 15: 3rd Twenty20, Wellington Regional Stadium, Wellington.
ODI series: Feb 17: 1st ODI, Seddon Park, Hamilton; Feb 20: 2nd ODI, McLean Park, Napier; Feb 23: 3rd ODI, Eden Park, Auckland.