Born at Waco, Texas, his mother was Loree Wilson (née Hamilton). His father D. M. Wilson, was a real-estate lawyer. Robert Wilson went to Waco High School from 1954 to 1959. At the age of 17 he was taken to a local dance instructor who it was hoped would cure his stutter. She was called Bird "Baby" Hoffman and wore an immaculate white dress and dyed her hair red. She was an inspiration to him and for a short while he called himself Byrd Hoffman.
Wilson was at the University of Texas from 1959 on a business administration course, but this was only to please his father and he dropped out in 1962. He then went to study interior design at the Pratt Institute, Brooklyn, from 1962 to 1964. While in New York he encountered mainstream theatre for the first time but disliked most of it. However, he did like the work of the choreographers George Balanchine and Merce Cunningham.
In 1964 during the rehearsals for one of his first plays Robert Wilson had a mental breakdown and spent six weeks in an institution in Texas. He returned to New York and began working with the choreographer Alwin Nikolais and designing the Motel Section of Jean-Claude van Itallie's America Hurrah.
Robert Wilson also continued with therapeutic work that he had started while at university to earn a living. He worked with mentally and physically disturbed children, and at a New York hospital he directed a ballet for iron-lung patients where the participants moved a fluorescent streamer with their mouths while the janitor danced dressed as Miss America.
He founded the Byrd Hoffman School of Byrds which consisted of mostly non-actors that Robert Wilson had found in the streets and burger bars. They met regularly at Robert Wilson's loft in Spring Street (later known as the Byrd Loft) and had communal meals, engaged in dance, and smoked marijuana. One of the Byrds was the dancer Andy de Groat who became Robert Wilson's long-term partner in the 1970s.
After A Letter for Queen Victoria, (1974-5), Robert Wilson dissolved the Byrds and started to use professional actors. Backstage of A Letter for Queen Victoria Robert Wilson met Philip Glass and they decided to work together. Over six or eight months they met each week in a restaurant and they eventually put together Einstein On The Beach, (1976).
Much of Robert Wilson's fees have been ploughed back into the Byrd Hoffman Foundation, a non-profit organisation that has supported his work.