The Minstermen are to move into the Monks Cross site in a year-and-a-half, sharing with York City Knights Rugby League Club.
The 8,000 capacity ground will also be a leisure sporting complex with a cinema and retail park also included in the project..
The Vanarama National League North club want to be promoted before moving into their new home in the summer of 2019.
City chairman McGill said: "We have waited a long time for this day to arrive so, naturally, I am delighted to see that work is getting underway at Monks Cross.
“It is great news for everyone associated with York City Football Club."
Councillor David Carr, Leader of City of York Council, added: “It is fantastic that construction workers are now on site delivering a Community Stadium and leisure complex for all our residents to enjoy.
“We have always been committed to delivering the Community Stadium and accompanying facilities which will be a great asset for the city.”