The former Trafford manager took over the reins at the struggling Premier Division side in October as the successor to Jon Robinson and decided to call it a day after the club suffered its first relegation in its 50 year history with six games to spare.
Vaughan's number two Wayne Goodison took charge of Tuesday night’s 2-2 draw with Colwyn Bay and officials at the Harry Williams Riverside Stadium say he will be in the dug-out for the final game of the season at home to Ilkeston on Saturday.
Former Trafford player and manager Vaughan helped lead the Shawe View side into the EVO-STIK Northern Premier League during a 16-year spell with the club. After leaving in November 2014, he was coaching at FC United of Manchester before joining the Rams.
Vaughan's first two games in charge yielded four points but he was ultimately unable to turn around a season which had started badly. After thanking him for his efforts, a Rams spokesman said: "The club wishes Garry all the best for the future."
Candidates for the post should send their CVs to Ramsbottom United chairman Harry Williams at 35 Nuttall Lane, Ramsbottom, Lancashire, BL0 9JX.
Follow us: @evostikleague on Twitter | Facebook www.facebook.com/evostikleague | The NPL Facebook Group www.facebook.com/groups/TheNPL/