While confirming his resignation, Anzhi quoted Hiddink as saying: "This decision was not easy for me, but I've always said that my mission at Anzhi may end when the club is able to develop and grow by itself, without my participation.
"Now that time has come. I am convinced that the club has a great future, and I'm glad I was part of this large-scale football project."
Hiddink, who has played a key role in the emergence of the Dagestan-based club built on the backing of billionaire owner Suleyman Kerimov, signed a new one-year deal last month but has opted to leave just two games into the current season, the second of them a defeat against Dynamo Moscow.
Replacing Hiddink at Anzhi is former Manchester United first-team coach Rene Meulensteen.
With Barcelona in the market for a new coach after Tito Vilanova, 44, stepped down to continue treatment for throat cancer, Hiddink was briefly made odds-on favourite to take over at the Camp Nou.
However the odds on former Chelsea boss Hiddink - who has also managed PSV, Fenerbahce, Netherlands, Real Madrid, South Korea, Australia, Russia and Turkey - have since cooled, with former Newell's Old Boys boss Gerardo Martino now expected to take the Barca job.