Sir Terry will join the company from Crossrail, where he has been the Chair since 2009.
As a former Chief Executive of Tube Lines, he has also held leading roles at BAE Systems, Rover Group and the Chartered Management Institute.
He will take over his new role from Sir David Higgins on 01 August.
Transport Secretary Chris Grayling said: "Sir Terry's appointment as Chair of HS2 ensures that we will continue to see world-class leadership in an exciting period for one of Europe's most significant infrastructure projects, helping deliver huge economic growth and improvements for passengers across the country.
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"His wealth of experience and expertise, demonstrated in numerous leading roles including overseeing the ambitious Crossrail project, as well as his respected reputation and enthusiasm, will be invaluable in the project's continued success."
Sir Terry Morgan said: "It is a privilege to take up this crucial role with HS2 – a railway that will help transform this country through better connections for over 300,000 passengers every single day.
"HS2 will be a driving force behind greater prosperity and productivity across the country, unlocking opportunities for growth and regeneration and building a transport network fit for the future. I look forward to meeting the team and beginning the vital work of taking this magnificent project from strength to strength."
(LM)
