The 66-year-old took charge of the Russian outfit in February 2012 and led the club to their best-ever league finish of third place in the Russian Premier League last season.
But the Dutch coach has opted to resign from his position, just two games into the new campaign, leaving compatriot and former Manchester United assistant coach Rene Meulensteen to take over the reigns with immediate effect.
In a statement on Anzhi's official website, Hiddink said: "This decision was not easy to me, but I've always said that my mission with Anzhi would end when the club is be able to develop and grow on itself, without my participation.
"Now it's time has come. I am convinced that the club has a great future, and I'm glad I was part of this large-scale project of football."
Anzhi - who were beaten 2-1 by Dynamo Moscow in their last league outing - have moved swiftly to promote Meulensteen to the hotseat after he originally joined the club as part of Hiddink's coaching staff, while thanking Hiddink for his efforts.
"Today, the general manager of the club, Ayvaz Kaziakhmedov, introduced the players to a new head coach - Rene Meulensteen, who joined the coaching staff before the start of the season and was involved in preparing the team for the championship," the statement added.
"The club sincerely thank Guus Hiddink for his significant contributions to the club and wish him success in his future career."
The former Real Madrid's boss future in the game now appears uncertain. Hiddink initially announced his retirement from football in November, at the end of the Russian Premier League season, before extending his contract with Anzhi by a further season, though he may now opt to make that decision permanent.