Shakib will take over the baton from ODI skipper Mashrafe bin Mortaza, who recently announced his retirement from the shortest format of the game.
The decision was taken in a BCB meeting in Mirpur's Sher-e-Bangla National Stadium on Saturday.
“Since Mashrafe has retired, the board unanimously agreed to appoint Shakib as Bangladesh’s next captain for T20Is,” BCB president Nazmul Hasan told reporters after the meeting.
“A few other names were discussed but in the end we all have agreed to appoint Shakib,” he said.
Nazmul did not give any timeframe for Shakib, who is expected to assume his role against Pakistan in July.
Shakib, who captained Bangladesh from 2009-11 in all formats of the game, has so far led the team in four T20Is, which they all lost.
With his appointment, Bangladesh have now three separate captains for three formats with Mushfiqur Rahim leading the Test side and Mashrafe at the helm of ODI side.
Among other agendas in the meeting were the increase in annual salary and match fee of the Bangladesh cricketers, along with the 2017 BPL T20.