The Austrian-born conductor became the orchestra's 15th music director in 2001, succeeding Christoph Eschenbach.
The decision lengthens Graf's current contract by three seasons, and follows last month's announcement of an agreement in which the orchestra's musicians will receive an increase in pay and insurance compensation over the next three years.
"The musicians are excited about continuing our work with Maestro Graf," the Chronicle reported Donald Howey, double bassist and president of the orchestra committee, as saying. "With every passing year, our relationship and understanding grow stronger."
Said the conductor, "it is a great feeling that we will go ahead in an atmosphere of excellent collaboration and confidence."
Graf studied in Italy and Russia before winning first prize in the Karl B‹hm Conducting Competition in 1979, making his Vienna Festival debut the following year.
In 1984, he was named music director of the Mozarteum Orchestra and the Landestheater in Salzburg. He made his American debut in 1989 with the Buffalo Philharmonic Orchestra.
Graf was previously the music director of the Calgary Philharmonic Orchestra, a position he held from 1995-2003.