The decision was taken in a meeting in Singapore on Tuesday.
Bangladesh Cricket Board (BCB) President Nazmul Hassan confirmed on his return from the meeting on Wednesday night that the country will organise the competition for the third successive time.
The tournament which features the hosts, India, Pakistan, Sri Lanka and an Associate, will begin on February 24 and the final will be held on March 6.
Asia Cup 2016 will for the first time have T20 matches as well considering the ICC World T20 is scheduled to begin five days after the event.
Bangladesh, who also hosted the 2012 and 2014 editions, will organise the tournament for a record fifth time ahead of Sri Lanka, who have hosted it four times.