The appointment comes as Roy Griffins retires after more than 10 years as chairman of London City.
The airport said Griffins had left the business “in excellent shape to fulfill its potential”.
Morgan is currently a non-executive chairman of Crossrail and Ricardo, and is a former executive in the UK infrastructure and defence space.
He was chief executive of Tube Lines from 2002-2009 and managing director of Land Rover vehicles in the early 1990s.
Morgan said: "I am delighted to be taking on this role at such an exciting period at London City airport with the City Airport Development Programme having been granted formal planning permission in 2016.
“I look forward to working with the board, shareholders and executive team to help the business to fulfil its potential over the coming years."
Griffins said: "Over the past 10 years London City has shown how much good a responsible, well managed airport can do for its neighbourhood, its city, the country.
“Between 2006 and 2016 the number of passengers using the airport almost doubled, from 2.4 million to over 4.5 million, reinforcing London City’s reputation as the UK’s leading business airport.
“I am proud to have been a part of that success story and I wish Sir Terry, the London City board and the executive team every success in the airport’s continuing journey."
David Fison also joined the London City airport board in January 2017 as an independent non-executive director.