Crossrail is a new rail link across the capital and beyond, connecting Essex in the east with Berkshire in the west and serving Heathrow airport.
Its first section was scheduled to open this month but will not now happen until late next year. It has also required multi-million pound bailouts from central government.
Morgan had led Crossrail since 2009, but was only appointed as HS2 chair four months ago.
Accepting Morgan’s resignation, transport secretary Chris Grayling said: “Sir Terry has been an integral part of Crossrail for almost a decade and I would like to thank him for his dedication and the expertise he brought to the role. I am also grateful to him for his work as chair of HS2 Ltd.”
Morgan had recently clashed with London mayor Sadiq Khan, suggesting that Khan knew of the problems with Crossrail well before the announcement of the delay. Khan has publicly refuted this.
In a statement on Morgan’s resignation, Khan said: “For a while now I have had concerns about the effectiveness of Crossrail’s governance.
“Not only was I angry when Crossrail informed us that the project would be delayed, but historically there has been a lack of adequate information shared by the senior Crossrail leadership with the project’s joint sponsors, namely the Department for Transport and Transport for London.”
He said the project’s new leadership must bring in a “renewed sense of urgency and transparency”.
Reports have suggested the Crossrail problems convinced ministers Morgan was not the right person to take HS2 forward. It is itself a controversial project with a price tag of almost £56bn.
Morgan will be replaced as HS2 chair by engineer Allan Cook.
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.”
An appointment to the Crossrail job has not yet been made.
