René Auberjonois's mother was Princess Laure Murat. On his mother's side, René is descended from Joachim Murat, King of Naples, and his wife Caroline Bonaparte, sister of the Emperor Napoléon. His father, Fernand Auberjonois (1910-2004), was a Cold War era foreign correspondent, and his grandfather, also named René Auberjonois, was a Swiss post-Impressionist painter. Auberjonois' family moved to Paris after World War II, where at an early age he decided to become an actor. When the family later moved back to the United States, it was to join an artists' colony in upstate New York whose other residents included Burgess Meredith, John Houseman and Helen Hayes. The environment only confirmed his decision to act, and he made important contacts that were to advance his career.

One of the most influential contacts Auberjonois made during this period was Houseman, who gave him his first job in the theater at 16 years old, as an apprentice. They worked together again later, when he taught under Houseman at the Juilliard School. He stated in a 1993 interview that Houseman was the person who had most influenced his career.

To complete his education, he enrolled at the Carnegie Institute of Technology (now Carnegie Mellon University). After graduating, he worked with several different companies, eventually landing a role on Broadway in 1969, where he played alongside Katharine Hepburn in Coco. He was presented with a Tony Award for his performance.

Auberjonois married Judith Mahalyi on October 19, 1963 with whom he has two children, Tessa and Remy.