His resignation comes after the island nation's back-to-back Test series defeats to continental neighbours Pakistan and India in last three months.
It is learned that Atapattu's resignation was accepted by Sri Lanka Cricket's interim chief, Sidath Wettimuny.
One of Sri Lanka's batting mainstay during his playing days, Atapattu was chief coach from September 2014, after Paul Farbrace took over as England assistant coach.
He also worked as the team's batting coach from 2011 and was the interim head coach for some time before being assigned full charge of the team.
According to reports, Sri Lanka Cricket is likely to approach former Sri Lanka batsman Chandika Hathurusinghe to take over the job as he did well with the Bangladesh national side.
Apart from guiding them to the quarter-finals of the ICC Cricket World Cup, Bangladesh beat Pakistan, India and South Africa in three successive ODI series.
The other name doing the rounds is of Graham Ford.
The 44-year-old Atapattu played 90 Tests and 268 ODIs, scoring 5502 and 8529 runs respectively.
Image: Marvan Atapattu
Photograph: Charlie Crowhurst/Getty Images
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