Domingo, who joined the Tigers as head coach in September 2019, announced his decision to the BCB just two days after losing the home Test series against India.
The BCB will now be looking to split the head coaching post between formats ahead of hosting England in three T20Is and three ODIs in March.
Jalal Yunus, BCB's cricket operations chairman, said on Wednesday: "He has resigned with immediate effect. He sent a letter to the board's CEO last night. He thanked the board for its support. He wished the team well.
"The deal with him will close according to the terms of his contract. You will definitely see a new coach before the England series (in March). We are already speaking to someone, but we will only disclose it when it is finalised.
"We are likely to have two coaches. One for T20s, and another for Tests and ODIs. To bring the overall coaching on the right track, we will appoint a high-performance manager or director.
"He will show the way forward for Bangladesh cricket. We are in talks with some candidates for that position too."
Under Domingo's tutelage, Bangladesh won T20I series against Australia and New Zealand at home, a Test match in New Zealand, an ODI series in South Africa and one at home against India.