The City of York Council Executive unanimously approved the plans and they have entered into legal agreements over the new stadium with Greenwich Leisure Limited.
The main construction phase is expected to take 16 months and it is hoped that the stadium will be ready for the start of the 2019/20 season.
The 8,000 capacity ground will house both York City Football Club and York City Knights Rugby League Club - supporting their long-term viability.
The £41m project features a cinema complex, including an IMAX screen, five restaurants, and three retail units which will be run by Cineworld.
Chairman Jason McGill said: "This is exciting news for York City supporters and the city's sporting future. It is a highly significant announcement which will help safeguard the long-term future of York City Football Club.
“I am extremely grateful to the local council and other associated parties for their hard work and patience in moving this matter forward."