Gergiev, 59, will replace Lorin Maazel as the orchestra's chief when Maazel's contract expires in 2015, the city council said in a statement released late on Wednesday.
The Moscow-born maestro, currently chief conductor of the London Symphony Orchestra and long-time director of the legendary Mariinsky Theatre in Saint Petersburg, will initially be appointed for a term of five years until 2020.
"Valery Gergiev is without doubt one of the most important, influential and inspirational conductors of our time," said Munich's culture minister Hans-Georg Küppers.
"His youthful energy and enthusiasm will not only benefit the orchestra. His ability and charisma will also shape audiences of all different age groups and Munich's musical life," Küppers said.
The appointment, voted through by a majority by Munich's city council on Wednesday, had been decided in consultation with the orchestra, he added.
"The Munich Philharmonic is a fantastic orchestra with a great tradition," Gergiev was quoted as saying in the statement. "We know each other very well. I'm happy that we can intensify our artistic collaboration."
Gergiev is one of the busiest conductors working today. He has headed the Mariinsky Theatre in St. Petersburg for 20 years and been chief conductor of the London Symphony Orchestra since 2007. He is also chief conductor of the World Orchestra for Peace, an initiative set up in 1995 by legendary maestro Georg Solti.
The classical music scene has been abuzz with speculation recently that Gergiev was to take the Munich position after the LSO in London announced last week that he would not be renewing his contract with them after the end of 2015.
But the London orchestra insisted that their relationship with Gergiev remained "excellent" and would continue to be strong even after his departure.
The Munich Philharmonic is one of Germany's top orchestras and its previous chief conductors include the legendary Sergiu Celibidache, US maestro James Levine and German star conductor Christian Thielemann.