"I have decided that I shall leave my role as National Bowling Coach when my contract expires at the end of the month," Streak was quoted as saying by a cricket website.
"I would like to thank the BCB for the opportunity afforded to me in 2014. It has been a thoroughly enjoyable experience and I will continue to follow Bangladesh's progress closely. I feel now is the right time for me and my family to make this decision and I look forward to the future as I look to continue my coaching career," said the former Zimbabwe captain in a statement.
The development comes days after Streak was reported to have applied for a coaching post at India's National Cricket Academy. He is also working as Gujarat Lions' bowling coach in the Indian Premier League.
Under the tutelage of Streak, who was appointed to the role in May 2014, Bangladesh won a Test series and two ODI series against Zimbabwe, and advanced to the knockout stage of the 2015 World Cup before winning maiden ODI series against Pakistan, India and South Africa in their home soil.
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