Worthington has signed a year's rolling contract and the former Northern Ireland boss said that he was "delighted" to stay at the club.
"I'm delighted to have got this sorted," Sky Sports News quotes Worthington as saying. "It's a lovely club, a family club and I'm delighted, obviously now that we managed to stay in the Football League.
"That was my number one remit when I came in with 10 games to go and the club have asked me to stay on. It couldn't have worked out better, but there is a lot of work to do during the summer.
"We'll pretty much start with a clean slate and the work is ongoing, but we believe there is plenty to build on here."
York finished the season in 17th after a 1-0 win away to Dagenham & Redbridge.