England will arrive in late January and will also play two Twenty20 matches against the home side.
"England will compete strongly in all three forms of the game and the series will build on our traditional rivalry with them ahead of the New Zealand tour there in May next year," New Zealand Cricket (NZC) chief executive Justin Vaughan said Tuesday.
Bangladesh will arrive in December and play two Tests, three one-day internationals and two first-class matches, Vaughan announced.
After playing only two Tests in the last southern summer in the lead-up to the World Cup, New Zealand will resume their international programme with a South African tour starting in November.
The two sides will play two Tests and five one-day internationals.
England arrive Jan 28; Feb 5: Twenty20 international in Christchurch; Feb 7: Twenty20 international in Auckland; Five one-day matches between Feb 9 and 23; March 5-9: First Test at Seddon Park in Hamilton; March 13-17: Second Test at Basin Reserve in Wellington; March 22-26: Third Test at McLean Park in Napier.