The appointment completes the new blood at the top of the agency, following the appointment of major projects director Nirmal Kotecha in April.
Graham is currently Director of Projects, National Networks, in the Department for Transport, responsible for the delivery of major rail investment projects including the Channel Tunnel Rail Link, the West Coast Route modernisation and Thameslink.
"I am delighted to take on the leadership of the Highways Agency. Millions of people rely on the Agency's road network every day, for personal and business travel and for moving freight.
"In recent years, the Agency has introduced a number of innovations to improve its service to customers, and help protect our environment. I look forward to working with both staff and stakeholders to make yet more progress on both," he said.
Graham is a fellow of the Institution of Civil Engineers, and joined Mouchel in 1988 as a Principal Engineer, working in the UK and abroad, including Qatar and Kuwait.
He moved to Bovis Lend Lease Consulting in 1995, and then to the Strategic Rail Authority in 2001 as Director of Projects.
He transferred to the Department for Transport in 2005, and now succeeds Archie Robertson at the helm of the Highways Agency.