He said his tenure with the team was 'thoroughly enjoyable'.
The former Zimbabwean fast bowler has decided not to extend his contract with the BCB which will end this month.
"I have decided that I shall leave my role as National Bowling Coach when my contract expires at the end of the month," Streak said in a statement.
"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."
He is the bowling coach of the Gujarat Lions in the ongoing IPL.
Indian daily ‘The Hindu’ reported a few days ago that Streak had applied for a coaching post at India's National Cricket Academy.
The report added NCA chief Niranjan Shah was very keen to get Streak's services.
Since then speculations swirled over the 42-year-old coach's departure.
Khan confirmed that the board was taking steps to appoint a suitable replacement as soon as possible.
On Monday, Akram said they were targetting Sri Lanka's Champaka Ramanayake, Chaminda Vaas, Pakistan's Aaqib Javed and India's Venkatesh Prasad. But no proposal was sent out as the board was waiting for an official announcement from Streak.