Some observers had expected officials to move the tournament out of Bangladesh following an outbreak of violent protests and strikes in the capital Dhaka ahead of elections Sunday.
"The tournament will go ahead as scheduled in Bangladesh from February 25 to March 7," Asian Cricket Council chief executive Ashraful Huq told AFP after an executive board meeting in Colombo.
"Everything is in place for the tournament, no one raised any issue about safety," Huq said, adding the Bangladesh Cricket Board had made a detailed security presentation at the meeting.
Election-related violence in Bangladesh has claimed more than 140 lives since late October, with opposition parties boycotting the polls and organising a series of blockades across the country.
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Afghanistan will join Asia's four Test nations -- India, Pakistan, Sri Lanka and Bangladesh -- in the 50-over tournament, Huq added.
The fast-improving Afghanistan team, which has qualified for their maiden appearance in the 50-over World Cup, have also made it to their third successive World Twenty20.
Bangladesh is also due to host the World Twenty20 tournament from March 16 to April 6.