The 8,000 capacity stadium at Huntington was due to open in August 2016 but will not be ready for occupation until around December, the club said.
York Council said it would work with the Minstermen to "minimise any impact to the club and its fans".
City said the delay would have "very little impact".
In a statement, it added: "Although some may be slightly frustrated that the club will not be in a position to move into the new stadium for the start of the 2016/17 season, ensuring the future development is built correctly is crucial in providing a fantastic new home for York City for decades to come."
But the good news is that York's rugby league club will now share the ground with the city's football team.
York City Knights said the move to York City FC's new 8,000 capacity stadium at Huntington was a "significant milestone" for the club.
The news marks the end of fraught negotiations between York Council and the rugby side over the new venue.
The authority said signing the new agreement was a "major step forward" for the project.
Rugby Club coach James Ford said the new training ground would help the players improve.
He said: "It can't be anything but positive to get those facilities and it won't take long before the evidence is in the performance."
Both teams will play at York City's ground at Bootham Crescent until the new stadium is complete.