The West Indies Cricket Board (WICB) said the two sides "mutually agreed to terminate their association" with team manager Richie Richardson stepping in as interim coach.
No reason was given for the departure of Gibson, who had been in charge since 2010 and led the West Indies to the World Twenty20 title in 2012.
However, West Indies are currently eighth in the Test rankings, the lowest among the established nations, eighth in the one-day rankings and seventh in the Twenty20 rankings.
"On behalf of the Board and West Indies cricket as a whole we express our gratitude to Ottis for his work," WICB chief executive officer Michael Muirhead said in a statement.
The WICB thanked Gibson for his "unwavering committment and professionalism" in his role as head coach, a position he occupied for four years and for which he had signed a contract extension only last year that would have taken him to 2016.
The highlight of Gibson's time in charge was the team's triumph at the World T20 in Sri Lanka in 2012. Their defence of the title last March in Bangladesh ended in defeat to eventual champions Sri Lanka at the semi-final stage.
Team manager Richardson, the former West Indies captain and middle-order batsman, will take over the coaching responsibilities for the Bangladesh series while a full-time replacement is confirmed.
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