Sir Philip has served as chairman since February 2009 and his departure will be in line with his long-standing intention to serve in the role for between five and seven years, according to an RBS statement.
It was announced simultaneously that Sir Philip will be appointed to the board of GlaxoSmithKline plc as a non-executive director with effect from 1 January 2015 and will assume the role of chairman from 1 September 2015.
"It has been a privilege to serve as chairman of RBS since 2009,” Sir Philip said.
“I am looking forward to working with my colleagues in the months ahead as we work to implement the bank's strategy and continue to improve the support we provide to our customers,” he said.
The process for selecting the next chairman of RBS is being managed by the board's nominations committee.
Last month, RBS was fined $25.7 million for serious failings in their advised mortgage business sales.