Tremlett, who has been with the squad throughout as a stand-by player, was the obvious man to come in for Broad as a like-for-like replacement.
Broad discovered yesterday that his side strain was serious enough to send him back to the UK and end his tournament.
He left his teammates behind in Chittagong this afternoon, and a few hours later the England and Wales Cricket Board confirmed their application to the International Cricket Council's event technical committee for Tremlett to come in as a seam-bowling reinforcement.
He is the second replacement player England have needed in the past two days, having summoned Eoin Morgan in place of the injured Kevin Pietersen on Monday.
Morgan, the middle-order batsman, joined the squad for practice at the Zahur Ahmed Chowdhury Stadium today, in preparation for Friday's Group B fixture against Bangladesh at the same venue.