The 50-year-old teams back up with Minstermen boss Wilcox, whom he worked alongside at Scunthorpe last year.
“I’m really excited about the opportunity of joining York City Football Club,” Schofield told the club’s official website.
“It is a lovely family club and one thing which really struck me when I met the chairman and the other board members for the first time was their enthusiasm to take it forward.
“The chairman is a gentleman who wants to progress and realises if that is achieved through gradual steps then it will be maintained for years to come.
“He has got some great plans for the football club and there are exciting times ahead for York City.”
Schofield made over 500 league appearances for Lincoln as a player and was head of youth development for seven years before taking up the role of first-team manager.
He has also worked in various coaching roles at Scunthorpe, Walsall, Cheltenham, Cambridge, Notts County and Gillingham.