"Please be informed that the Sri Lanka national team will be touring Bangladesh from 24th January 2014 till the end of Asia Cup," Sri Lanka Cricket (SLC) said in a statement.
The Sri Lankans will leave for Dhaka on Friday and play the first Test from January 27, the SLC said, adding that there will be two Tests, three ODIs and two Twenty20 games during the tour as originally planned.
The decision came after a security assessment visit to Dhaka by two senior SLC officials.
The T20 World Cup is to follow the five-nation 50-over Asia Cup that involves hosts Bangladesh, Afghanistan, Sri Lanka, India and Pakistan.
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"We have assurances from the Bangladesh security forces that there will be a very high level of security," an SLC official said asking not to be named.
"We are also told that rival political parties have said they also want the tournaments to go ahead and have given an undertaking that cricket will not be targeted."