Guillaume was born as Robert Williams in St. Louis, Missouri. He studied at St. Louis University and Washington University and served in the United States Army before pursuing an acting career. He made his Broadway debut in Kwamina in 1961. Other stage appearances included Golden Boy, Tambourines to Glory, Guys and Dolls, Jacques Brel is Alive and Well and Living in Paris, Phantom of the Opera (succeeding Michael Crawford in the lead role), and Purlie Victorious, for which he won a Tony Award.

Guillaume made his television debut in the series Soap, playing Benson DuBois as a butler on that series from 1977 to 1979 and then on a spinoff series, Benson, until 1986. He won Emmy Awards for both series, in 1979 and 1985. He also appeared as marriage counselor Edward Sawyer on The Robert Guillaume Show (1989), Detective Bob Ballard on Pacific Station (1991), and television executive Isaac Jaffe on Sports Night (1998-2000). Guillaume suffered a mild stroke on January 14, 1999, while filming an episode of the latter series. He recovered and his character was later also depicted as having had a stroke.

Guillaume has also appeared in a number of films, including Seems Like Old Times (1980), Lean on Me (1989), First Kid (1996), and Big Fish (2003). His distinctive voice has also been used for characters in television series Captain Planet and the Planeteers, Fish Police, and Happily Ever After: Fairy Tales for Every Child and for the voice of Rafiki in the movie The Lion King and its sequels and spin-offs. He also supplied the voice for Eli Vance in the 2004 video game Half-Life 2.

Guillaume has his own star on the St. Louis Walk of Fame.