Dr Burgess said in a statement that his wife's mother is seriously ill and he will return to his home in Annapolis, Maryland in early September to support her, after finishing up at Telstra at the end of this month.
He will be replaced by David Quilty, who has been Telstra's director of government relations since January 2006.
Dr Burgess, who joined Telstra when Sol Trujillo became chief executive in 2005, expects to resume his life as an advisor to business and government on matters related to technology and society.
"The last three years have been enormously consequential for Telstra and Australia with the full privatisation of Telstra, construction of the world's largest, fastest, and most advanced wireless broadband network and the transformation of Telstra," Dr Burgess said.
"Working in a country and culture not your own is an enormous privilege and working for one of its iconic companies is a privilege amplified.
"My time in Australia and with Telstra has been one of the most memorable experiences of my life, both personally and professionally."
Dr Burgess said he had increased the capacity of Telstra to communicate with consumers and the public, represent shareholder interests, put high-speed broadband on the agenda three years ago, and transformed the way the company communicated both internally and externally.
"It was hard for some to give up the idea that Telstra is community property," he said.'
Telstra had been criticised by some for its aggressive approach to defending its investments from "value-destoying" regulation.
"Our new approach achieved important results, including safeguarding new investments like NextG and ADSL2+ from value-destroying regulation, winding back regulation on more than four million copper telephone lines, and the reversal of a $1 billion taxpayer gift to SingTel-Optus," he said.
Trujillo thanked Dr Burgess for his enormous contribution to Telstra over the past three years.
"Phil has great integrity and has not been afraid to show leadership, often speaking the truth even when it was inconvenient for established interests to hear it," Trujillo said.
Dr Burgess will continue to serve as a consultant to Telstra and advisor to Trujillo.
Meanwhile, he will return to the Annapolis Institute to resume research, writing and speaking on issues related to technology and society.
Dr Burgess has also been appointed as a Senior Fellow at the Center for the Digital Future at the Annenberg School for Communications at the University of Southern California in Los Angeles.
