The National League North club have won three promotions in three years, all as champions.
But it has been decided a change of direction is now required.
The Bulls sit 12th in the table with a return of 11 points from eight matches.
Hereford lost 2-0 at Brackley last weekend, their third defeat in four games.
"This is not a decision the board has taken lightly and it is one made with a heavy heart. However, the directors are in unanimous agreement that now is the right time to make a change," said chairman Ken Kinnersley.
"While recent results have been disappointing, this is a decision taken more with the long-term goal of progressing to the Football League in mind and we feel it will give the club the best possible chance of continuing the positive progress it has made so far.
"We’d like to sincerely thank Pete for all his hard work over the past three seasons and no-one here will ever underplay his achievement in securing three championship wins in three seasons and a Wembley appearance having had to build a squad from scratch. We will always be grateful for all the happy memories he has given everyone who cares about this club.
"Every fan will remember the vital role he has played in creating the momentum that we are aiming to retain for as long as possible and I’m sure everyone who cares about this club will join me in wishing Pete all the very best for the future.
"In terms of what happens next, we will provide an update to supporters via the club’s official website as soon as plans are finalised."