The appointment of Sawford, who lost his Corby seat to Conservative Tom Pursglove in last month’s general election, will see CEO Gill Morris take the role of executive chairman.
Connect said Sawford will have a leading role in the agency’s expansion. In December, the agency announced plans to enter new markets including the US, EMEA, Australia, China and India, expanding beyond its long-standing focus on Westminster and Whitehall.
Sawford won the Corby seat in a by-election in 2012. Before becoming an MP, he was previously a director at Connect and was also chief executive of the Local Government Information Unit (LGIU).
Morris said: "Andy brings a wealth of experience and a great track record. He will really strengthen our team and help me take Connect forward to bigger and better things."
Sawford said:"Connect is a great company – in my view it is the best in the business and is primed for even greater success and growth in the years ahead."
During his time in Parliament, Sawford was shadow minister for local government and cities, and served on the CLG Select Committee.