Sir Terry, who was chairman of HS2 for just four months, will be replaced by Allan Cook, former chairman of consultant Atkins prior to its acquisition by SNC-Lavalin.
A new chairman for Crossrail will be announced in due course.
Transport Secretary Chris Grayling said: “HS2 is the country’s biggest infrastructure project and, with his wealth of experience, Allan Cook CBE is the right person to oversee the project as it progresses towards full construction.”
Cook began his career as an apprentice electrician with his father’s contracting business. He is a chartered engineer with more than 40 years’ international experience in the infrastructure, automotive, aerospace and defence industries.
Before joining Atkins, where he was chairman for seven years, he was chief executive of defence firm Cobham until the end of December 2009. Prior to this he held senior roles at GEC-Marconi, BAE Systems and Hughes Aircraft.
His experience also includes acting as a former lead non-executive director for the then-Department of Business, Innovation and Skills under the coalition government and chairman of the Sector Skills Council for Science, Engineering and Manufacturing Technologies.
Cook said: “It is a privilege to be asked to take on this crucial role on UK’s biggest infrastructure project.
“HS2 has made impressive progress in the past 18 months – with 7,000 highly skilled people currently working on this project. The regeneration of the West Midlands and Curzon Street in Birmingham are now well underway.
“I’m looking forward to working with Mark Thurston, his team and our partners, getting ready for the next few years when we will be making significant progress on building HS2 for the future.”