Pybus, 48, told the Bangladesh Cricket Board (BCB) of his decision on Tuesday night, just weeks before the team take on the West Indies in a home series starting in November.
"We have already appointed Shane Jurgensen, the national team's bowling coach, as the interim coach for the team," BCB spokesman Jalal Yunus told AFP.
Pybus, who had two spells with Pakistan, could not be contacted for comment.
In an interview with ESPNcricinfo, he said the BCB wanted him to spend 320 days a year with the Bangladesh team, a commitment he was not ready to make because of family reasons.
Yunus said differences over some terms in the agreement meant Pybus had coached the team since June without signing a formal contract.
Pybus turned to coaching in his mid-twenties after injury halted his playing ambitions. He coached in South Africa before taking over the Pakistan team between 1999 and 2001 and in 2003.
Australian Jurgensen now has a difficult task to prepare the side less than three weeks before the first Test against the West Indies on November 13.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ