Mr Burgess has worked in the position for three years and overseen a significant period of modernisation within the firm.
Alan Trotter, finance director of Alliance Trust, will take Mr Burgess’ role on a day-to-day basis until a replacement is appointed.
Lesley Knox, chairman of Alliance Trust, said: “I would like to thank Robert for his contribution and the work he has done in developing Alliance Trust Savings since he joined in February 2009. He has built an experienced management team who are in a strong position to capitalise on the opportunities provided by the RDR.”
Mr Burgess said: “I have thoroughly enjoyed my three years at Alliance Trust Savings, during which time the business has seen strong customer and revenue growth and is increasingly recognised as a leading player in its sector.
“I am confident that Alliance Trust Savings is now well positioned to continue this momentum. I wish the team and the business continued success.”
No reason was given for Mr Burgess’ departure.