Gibson will replace South African Charl Langeveldt who had resigned from the bowling coach position in December 2019.
"He brings in tremendous experience and has coached or played all over the world," said BCB CEO Nizam Uddin Chowdhury in a press release. "He has also had the opportunity to observe Bangladesh cricket from close. I am sure he will be a very valuable addition to the Bangladesh Team's coaching group."
Since his retirement as a player in 2007, Gibson has held coaching positions including the head coach's role with the West Indies and South Africa and bowling coach of England.
Gibson's assignment with Bangladesh starts immediately as he will join the squad for the Pakistan tour. Bangladesh are set to play three T20Is, two Tests and an ODI in Pakistan between January and April. The T20I series will be played from January 24-27, followed by the first Test from February 7 to 11.
Bangladesh will then return to Pakistan in April for the one-off ODI which will be played on April 3 and the second Test from April 5-9.