Former Manchester United coach Rene Meulensteen has been named as his replacement already, and will take charge with immediate effect.
Barcelona need a new coach because Tito Vilanova has stepped down in order to undergo further treatment for cancer.
Hiddink guided big-spending Anzhi to third place in the league - the highest finish in their history - and also reached the final of the Russian Cup last season.
The Dutchman agreed a one-year contract extension only last month but just two games into the new Russian season, Hiddink has resigned.
Bookmakers reacted by slashing the odds on the former Chelsea boss to become the new head coach at Barcelona.
Hiddink has played a key role in the emergence of the Dagestan-based club built on the backing of billionaire owner Suleyman Kerimov.
In a statement on the club website Hiddink said: "This decision was not easy for me. I always said that my mission at Anzhi could end when the club was able to develop and grow on its own, without my participation. Now that time has come."
"I am convinced that the club has a great future and I am glad I was part of this large-scale football project."
An Anzhi statement read: "FC Anzhi has accepted the request of the head coach to terminate their employment relationship.
"The club sincerely thanks Guus Hiddink for his significant contribution to the club and wishes him success in his future career."
Hiddink's replacement Meulensteen was on Sir Alex Ferguson's staff at Manchester United until last month, and was one of the candidates for the Wigan job when it was vacant.