It is part of a restructuring that will also cut 400 corporate jobs, coming to a fifth of the company's corporate positions.
The move is expected to save about $55 million annually.
Approximately two-thirds of the reductions will take place immediately with the balance by the end of fiscal 2020.
Standley has been CEO since 2010 and will remain in the post until a successor is named.
Chief Financial Officer Darren Karst and Chief Operating Officer Kermit Crawford will also leave the company.
"Rite Aid’s Board of Directors is committed to more closely aligning the structure and leadership of the Company with our present scale and today's announcement is an important step in positioning Rite Aid for future success,” said Bruce Bodaken, chairman of Rite Aid’s board of directors. “These are difficult decisions and we recognize the implications they have for individuals across our organization. However, it is imperative we take action to reduce the cost of current operations and become a more efficient and profitable company.”
Rite Aid sold more than 1,900 stores to Walgreens Boots Alliance in 2017.
The company has reported losses in three out of the last four quarters.
The company and U.S. grocer Albertsons had terminated a $24 billion merger in August last year after Rite Aid's shareholders opposed the deal.