Das will now be in charge of the T20I side as the 50-over format with Tamim suggesting that Mehidy's performances had dipped since he got the leadership role.
Under Mehidy, Bangladesh played 20 ODIs with them winning 10, including four straight series victories at home against the West Indies, Pakistan, New Zealand and Australia.
Speaking after having a meeting with board of directors, Tamim said: "We had three captains across the three formats. I believe, and the board also believes, that having two captains is the right way forward.
“There is nothing right or wrong about either approach, but we feel two captains make more sense, one for white-ball cricket and one for red-ball cricket. That's why we've decided to appoint Litton Das as the white-ball captain, while Najmul Hossain Shanto will continue as the red-ball captain.
"Towhid Hridoy will be the white-ball vice-captain, while the red-ball vice-captain remains unchanged (Mehidy is currently the Test vice-captain)."
Tamim added: "Miraz (Mehidy) has been a highly successful captain. He won four of the last five series he led. But I believe we need Miraz more as a cricketer than as a captain. As a performer, we're used to seeing him at a certain level, and perhaps there had been a slight dip.
"While he has been doing well with the bat, we feel there's still room for improvement in his bowling,” he said. I've made it clear that we value him more as a cricketer.
"The outside noise may have been affecting him. He did a good job as captain, but we want him to perform at his absolute best. Besides, we felt having two captains across the three formats makes more sense than having three different captains."
Bangladesh head coach Phil Simmons admits his team "let ourselves down" after collapsing to 54 all out and a defeat in a three-day practice match ahead of the Test series against Australia.
Australia top-order batter Marnus Labuschagne is well rested ahead of bumper 18 months of Test cricket.
Bangladesh received a welcome boost ahead of the Test series in Australia after Litton Das was declared fit and added to the squad for the two-match series.
Bangladesh chief selector Habibul Bashar admits "there was a bit of desperation" after recalling Soumya Sarkar for the Test series in Australia, despite a five-year absence in the longest format.
