The current chairman, Peter Gyenes, becomes lead independent director of the company.
"Steve has been an outstanding leader for Sophos," said Mr Gyenes.
"Under Steve's leadership, the company has delivered strong revenue growth, built a comprehensive product portfolio, and successfully entered a number of high-growth market segments, including UTM, mobile device management, and cloud encryption.
"The board appreciates Steve's contribution to the success of the company, and we are delighted that Steve will continue his involvement as chairman."
"I look forward to working closely with Kris and the board as we continue to build on Sophos' global success."
Mr Hagerman was previously executive vice president, storage and server management at Veritas; then group president, data centre management at Symantec; and in 2008 was appointed CEO of Corel.