The former Netherlands coach took over from Holger Fach in November but only managed to take 18 points from his 18 games in charge, leaving Mönchengladbach one point above the drop zone. His decision to resign means he will not receive any compensation. Assistant coach Pim Verbeeck will also leave.
The 57-year-old said: "The wellbeing of the club is the most important thing at the moment.
I hope I can take the pressure off the players by resigning. Hopefully it will help the club avoid relegation."
Köppel steps up
Mönchengladbach president Rolf Königs added: "Dick Advocaat made the decision. We accept and respect it and would like to thank him for the work he has done." Advocaat will be replaced by Horst Köppel, who will step up from his role at the helm of Mönchengladbach's Under-23 side.
©UEFA.com 1998-2017. All rights reserved.