The ECB carried out a security review in the country following a series of deadly attacks, and consulted with players and officials on Thursday.
England play two Tests and three one-day internationals between 7 October and 1 November.
The matches will take place in Chittagong and Dhaka, where 20 hostages diedwhen a cafe was attacked in July.
Australia postponed their Test tour of Bangladesh in October 2015 over security concerns.