The 51-year-old former Norwich and Northern Ireland boss, who replaced Gary Mills at Bootham Crescent in March, has accepted the club's offer to stay in charge on a rolling contract. Assistant Steve Torpey will continue alongside him.
"I'm delighted to have got this sorted," Worthington told Press Association Sport. "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 on-going, but we believe there is plenty to build on here."
Worthington steered the Minstermen to four wins and two draws in their last six matches and they guaranteed themselves a second season in the Football League following promotion last season with a 1-0 win at Dagenham on the final day.
Chairman Jason McGill said: "We were only interested in one person taking this club forward and that is Nigel Worthington.
"During his time in charge of our last 10 games of the season he displayed exceptional managerial skills and impressed us with his work ethic and total professionalism."
McGill added: "There is much hard work to be done to prepare for the new season ahead. We're very pleased to have a manager in place who can help us to improve the club and build for a better future."