"Dav Whatmore has conveyed to the Bangladesh Cricket Board (BCB) that he will leave the post but will continue to work during the home series against India," Bangladesh media manager Rabeed Imam said.
The 53-year-old Whatmore guided Bangladesh to Super Eights in the ongoing World Cup where they finished seventh after losing six of their matches.
They beat India in the preliminary stages to qualify for the second round for the first time since making their World Cup debut in 1999.
They also defeated South Africa by 67 runs in the Super Eights.
Whatmore had upset Bangladesh officials by publicly stating that he would be interested in taking over from Greg Chappell as coach of India.
"Dav Whatmore has cited personal reasons for his decision for not renewing the contract but has agreed to extend his contract by one month in order to help the team to prepare for the India series," said a BCB release.
India play three one-day internationals and two Tests on their tour of Bangladesh starting in the second week of May.
"The BCB would like to put on record Dav's contribution to cricket in especially raising the standard of performance of the team at international level," said the statement.
Whatmore, who played seven Tests for Australia, also guided Sri Lanka to their only World Cup title in 1996. He took over as Bangladesh coach in 2003.
The BCB has formed a committee to chose a new coach for the team which will be announced shortly.