Broad, who sits fifth in the list of all-time leading wicket-takers in international test cricket, missed England's recent historic 3-0 series win in Pakistan due to the birth of his first child.
He returns to the setup alongside fellow seamers Matthew Potts and Olly Stone but paceman Mark Wood is not included and neither is Ahmed, fresh from becoming England's youngster-ever wicket-taker on debut in the third test win over Pakistan.
The youngster will go to the UAE T20 League in January with a view to joining up with England's white-ball team in Bangladesh in March. The ECB said the leg spinner's omission was part of "managing his winter".
Yorkshire and England batter Joe Root will play a handful of matches in the UAE T20 League ahead of the tour to New Zealand. He will then have a short break before joining up with the test team. Jonny Bairstow is also absent as he continues his recovery from a broken leg.
The first test begins in Tauranga on February 16, with the second taking place in Wellington on February 23.
Squad:
Ben Stokes (Durham) Captain, James Anderson (Lancashire), Stuart Broad (Nottinghamshire), Harry Brook (Yorkshire), Zak Crawley (Kent), Ben Duckett (Nottinghamshire), Ben Foakes (Surrey), Will Jacks (Surrey), Dan Lawrence (Essex), Jack Leach (Somerset), Ollie Pope (Surrey), Matthew Potts (Durham), Ollie Robinson (Sussex), Joe Root (Yorkshire), Olly Stone (Nottinghamshire)
