The 61-year-old told the Bulls' official website: "In view of our relegation from League One, I've taken the decision to step down from the post of team manager at the end of the season.
"Whatever mitigating circumstances there may have been which led to the disappointing season it's the manager who must ultimately take responsibility for results. That I have done.
"I'll continue in the role of director of football, which will be much more of an administrative position, and as chairman.
"I sincerely hope that this will not be my last managerial post but at present I'm totally committed to providing the new team manager with the necessary resources for success and to ensuring that all the hard work that's gone into the club over recent seasons will continue, providing the club with a prosperous long-term future.
"The position of team manager will be offered to present first-team coach John Trewick. He's a very experienced and respected football man who's capable of having an impact on the players and giving the club the impetus to put us into contention for a quick return to League One."