The Bangladesh Cricket Board (BCB) said Streak, who has been linked with a coaching post at India's national academy, informed them of his decision via email.
"I have decided that I shall leave my role as a national bowling coach when my contract expires at the end the month," Streak said in a statement via his agent on Twitter yesterday.
The Zimbabwean coach, who signed a two-year contract in 2014, has been credited with the steady progress made by Bangladesh's fast bowling unit, which contributed to the team's successful run in one-day internationals.
Bangladesh reached the knockout stage of the Cricket World Cup for the first time in 2015 and they beat Pakistan, India and South Africa in the same year to qualify for the 2017 ICC Champions Trophy in England.
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Akram Khan, cricket operations chief of the BCB, said they would appoint a new coach as soon as possible, with West Indies great Curtly Ambrose among the possible replacements.
Sri Lankans Champaka Ramanayake and Chaminda Vaas, Pakistan's Aaqib Javed, Venkatesh Prasad of India are also possible replacements for Streak, Khan said.