"On behalf of the Board and West Indies cricket as a whole we express our gratitude to Ottis for his work, particularly in coaching the team to winning the ICC World Twenty20 in 2012, and offer our best wishes to him in all his future endeavours," WICB chief executive Michael Muirhead said.
Former captain Richardson, currently the team manager, will take the reins against Bangladesh, with the first one-day international match on Wednesday in Grenada.
The move follows changes to the national selection panel earlier this month with former captain Clive Lloyd taking over.
Clyde Butts, the previous chairman of the selection panel, and Robert Haynes made way for the new panel members, who also included former fast bowlers Eldine Baptiste and Courtney Walsh.
Gibson took over the West Indies coaching job in 2010 after quitting as England's bowling coach.
Despite guiding the team to a maiden World Twenty20 trophy in 2012, the Caribbeans have continuted to toil in tests, and lost series to New Zealand home and away and also against India over the past 12 months.
West Indies are ranked eighth in tests out of 10 nations and eighth in ODIs.
They take on Bangladesh for three ODIs, one T20 international and two tests.
(Reporting by Sudipto Ganguly; Editing by Ian Ransom)
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