The 26-year-old Mortaza takes over from Shakib Al Hasan, who led the side in the recent Test series against England.
"Shakib was relieved of the responsibility as we felt he needs some break. He will continue as a player and will act also as a vice-captain on the tour," BCB spokesman Jalal Yunus said.
Mortaza was first appointed Bangladesh captain in 2009 for a tour of West Indies [ Images ] but his reign lasted barely two-and-half days when he fell awkwardly while bowling in the first Test in Kingstown.
Mortaza, who underwent surgery on both knees, returned to competitive cricket this year and was in the Bangladesh squad at the World Twenty20 [ Images ] in West Indies and the recent Asia Cup in Sri Lanka [ Images ].
Bangladesh start their tour with warm-up matches against Sussex and Middlesex before the first of three internationals against England on July 8.
They play Ireland twice in Belfast and end the tour with one-dayers against Scotland and the Netherlands on July 19 and 20 in Glasgow.