In 13 years of first-class cricket, Broom averages 39.32 with 18 centuries over 135 games. In one-day cricket he goes at 38.61 with seven centuries.
"I appreciate everything Derbyshire have done for me and have really enjoyed my time with the club," said Broom.
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"At the end of the day I couldn't pass up the opportunity to represent New Zealand and am excited about the opportunity to play international cricket again. It's the ultimate."
National selector Gavin Larsen said Broom brought plenty to the squad.
"Neil was the top run-scorer in the Ford Trophy competition last year, with an average of 84.66. He has an impressive strike-rate and obviously fills the No 4 role with Ross Taylor out injured."
Ronchi had an extended stint as one-day gloveman, but his form with the bat fell away badly.
He's recaptured some of that - he made a first-class century at better than run-a-ball against Otago around the time he discovered he'd been dropped from the national team, and made an unbeaten 58 off 31 balls for Wellington in their Super Smash loss to Canterbury last night.
''At this stage we see him as the best ODI gloveman in the country and the leadership he brings to the group is also immensely valuable," Larsen said.
That, however, clearly wasn't the case when he was dumped for Watling for Australia.
Jimmy Neesham is over his bruised right arm, courtesy of a Mitchell Starc short-pitched ball in Canberra on December 6.
Whether he retains the No 4 spot, in which he made a strong case for staying there in Taylor's absence in Australia, or it goes to Broom, or even Colin Munro, will be among the more intriguing side issues before the opening ODI.
Larsen pointed out there are just six players in this group from the World Cup squad of last year.
''It's important we give the new players the opportunity to feel comfortable on the international stage."
Fast bowler Lockie Ferguson is retained from Australia, where he showed he is quick but did get collared by Australia's senior batsmen in a tough learning experience.
The team come into camp on December 23-24 in Christchurch.
New Zealand's other two ODIs against Bangladesh are in Nelson on December 29 and 31 before three T20 internationals, for which a fresh squad will be picked.
New Zealand team for the three-game ODI series against Bangladesh starting in Christchurch on Boxing Day:
Kane Williamson ©, Martin Guptill, Tom Latham, Jimmy Neesham, Neil Broom, Colin Munro, Colin de Grandhomme, Luke Ronchi, Mitch Santner, Matt Henry, Tim Southee, Lockie Ferguson, Trent Boult.