Mr Anderson held the chief executive post at Optus for seven years, a period which included the company's acquisition by SingTel.
SingTel president and chief executive officer Lee Hsien Yang said Mr Anderson had made an outstanding contribution to the growth and development of Optus.
"Chris has led Optus for seven years through a remarkable period in its history, playing a major role in its financial transformation into one of the most successful companies in Australia," Mr Lee said.
"He has overseen Optus' evolution into a major force for competition and regulatory reform in the telecommunications sector."
Mr Anderson said he had enjoyed a great period at Optus with the company now trading strongly.
Mr Anderson will be replaced by Optus' current chief operating officer, Paul O'Sullivan.
Mr O'Sullivan, who will take up the chief executive's post on September 1, has been chief operating officer at Optus for two and a half years. Previously he was managing director of Optus Mobile.
Mr O'Sullivan is currently also on the board of Bharti Tele-Ventures Ltd, a SingTel Group member company, and is on the SingTel group management committee.
Prior to joining Optus, Mr O'Sullivan worked with the Colonial Group and Royal Dutch Shell.
He holds an economics degree from the University of Dublin and is a graduate of Harvard Business School's advanced management program.
Mr O'Sullivan said he was delighted with his new appointment.
"It has been a privilege to work with Chris' experience, the company has benefited greatly from his leadership," he said.
"I am very much looking forward to taking Optus on the next stage of its journey." AAP