The Asian Cricket Council met in Colombo on Saturday and in addition to confirming Bangladesh as hosts, it announced that Afghanistan would be included in an expanded five-team one-day international tournament.
"As of now, the decision has been made that Bangladesh will retain hosting rights of the Asia Cup," Bangladesh Cricket Board's acting chief executive Nizamuddin Chowdhury told reporters.
"We had a good meeting with ACC board members and they have been convinced that we can host the tournament."
The tournament had been in jeopardy after unrest in Bangladesh ahead of the country's parliamentary election on Sunday.
Last month the West Indies Under-19s team pulled out of a tour following an explosion near the team's hotel while Sri Lanka Cricket is still awaiting an internal security investigation before committing to their upcoming bi-lateral tour.
There is also some doubt over whether Bangladesh will host the World Twenty20, which is due to begin on March 16.
The ACC's decision to retain the Asia Cup in Bangladesh reportedly came after the BCB submitted a detailed security plan at Saturday's summit.
After the meeting, the ACC also revealed in a statement that Afghanistan would play in a major tournament for the first time.
"The board has decided to invite Afghanistan to participate in the Asia Cup 2014," it read.
"Afghanistan will now join Bangladesh, India, Pakistan and Sri Lanka. Afghanistan will be participating in a major ODI tournament for the first time which will give them an opportunity to get the experience of competing in a major tournament ahead of their ICC WT20 and ICC Cricket World Cup 2015 participation.
"A total of 11 matches will be played with the opening game on 25th February and the final on 8th March 2014."