Morgan has been Crossrail chairman since 2009, and was formerly Tube Lines chief executive.
He is the second former Crossrail executive to join the HS2 board following former chief executive Andrew Woolstenholme who became a non-executive director earlier this year.
Morgan said: “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.”
Mark Thurston, HS2 Ltd Chief Executive said: “As we continue the process of moving from design to construction, HS2 is stepping up a gear.
“In our short history we have contracted over 2,300 small, medium and large firms across the country and that process is only going to keep picking up pace in the next few years. As we continue to evolve as an organisation to meet that challenge, the guidance and direction that Terry will bring to his role will be vital.
“We will shortly also announce the appointment of a Chief Operating Officer and Chief Finance Officer — further signs of HS2 getting ready for the challenge ahead.”