Stretton, born in Canberra, began his career as a tap dancer, and was twice named national champion before switching to ballet at age 17. He began his studies at the Australian Ballet School in 1971 and joined Australian Ballet in 1973.
In 1978, he was made a principal dancer, and danced the lead male roles in the company's classical repertoire, including Swan Lake, Giselle, La Fille mal gard_e, Sparticus, and Onegin.
Stretton came to the United States in 1979 and joined first the Joffrey Ballet and then American Ballet Theatre, and also toured with Mikhail Baryshnikov's company Baryshnikov & Co.
After retiring from performing in 1990, Stretton worked for ABT and then returned to Australian Ballet in 1997 as its artistic director. He is credited with expanding the company's range to include new commissioned works by James Kudelka and Twyla Tharp, as well as works by William Forsythe and Jir‹ Kylišn.
Stretton was artistic director of the Royal Ballet in London for a year, from 2001 to 2002, and returned to Australia afterward.