Leigh trained at the Australian Ballet School before graduating to the Australian Ballet Company in 1970 and took part in the first Australian Ballet Choreographers Workshop that same year. Within two years he had reached soloist status. In his second year with the company he was awarded the first Churchill Scholarship for the Performing Arts, which he completed at the Juilliard School of Music, New York. Whilst studying in New York he performed with the Juilliard Ensemble, Janet Soames, Daniel Lewis, Sara Sugihara and others.
In 1975 Leigh returned to Australia for a season with the Dance Company of NSW. Later that same year he returned to Ballet Rambert London where he spent the next four years. He choreographed two ballets for Rambert as well as presenting two full evenings of his own choreographic work at the Riverside Studios. After a performance in Paris Jiri Kylian invited Leigh to join Nederlands Dans Theater (NDT) where he remained until his retirement from dancing in 1984. While with NDT Leigh choreographed two ballets and acted as teacher of contemporary technique for the NDT Junior Company.
After two years as freelance choreographer Leigh returned to Australia and in 1986 became Lecturer in Dance at the Victorian College of the Arts. He was appointed Artistic Director of the Australian Dance Theatre, Adelaide in 1987. He spent six years developing an extraordinary ensemble of dancers with a dominantly Australian repertoire whilst creating 14 works and touring the company throughout Australia and overseas.
In 1993 Leigh formed his own company Leigh Warren and Dancers. The company has performed for audiences in Holland, Singapore, London, Indonesia, Korea and all states of Australia. ABC TV has filmed a number of Leigh's works and in 2000 he was choreographic adviser for Spectre de la Rose in Paul Cox's film The Diaries of Vaslav Nijinsky.
Leigh and the company have received numerous awards, including the 1997 inaugural Adelaide Critics Circle award for outstanding achievement by a group, the 1999 Australian Dance Awards for choreography, most outstanding performance by a dance company and most outstanding performance by an individual dancer, the 2000 Sidney Myer Performing Arts Award for a Group, and Green Room Awards in 2001 for Best Male Dancer, Best Female Dancer and Best Ensemble. In 2001 Leigh was commissioned by the Melbourne Festival to produce a work in co-operation with William Forsythe, Artistic Director of Frankfurt Ballet. The resulting work, Quick Brown Fox, premiered at the 2001 festival. In 2002 he directed and choreographed his first opera, Akhnaten.