''In return New Zealand will visit Bangladesh in October next year,'' BCB general-secretary Mahbub Anam told Reuters.
Both series will be in addition to the International Cricket Council's (ICC) Future Tours Programme.
''New Zealand have agreed to play against us after seeing our performances in the World Cup,'' Anam said.
Bangladesh beat India and Bermuda in the group phase to reach the Super Eights in the Caribbean, but could only manage an upset victory over South Africa in their six subsequent matches to finish seventh in the World Cup standings.
Sri Lanka confirmed they would play three tests when they host Bangladesh in June, Anam said. It will be the second time Bangladesh will have played three Tests in a series after their maiden three-Test rubber against Pakistan in 2003.
Bangladesh's last Test was against Australia in April 2006 but they host India for two Tests and three ODIs this month.