Purnell has been in the post for 16 years.
His association with the BRB began in 1973, as a dancer with what was then Sadler's Wells Royal Ballet. He returned as an administrator and oversaw the company's relocation to Birmingham in 1990 and its separation from the Royal Opera House in 1997.
According to the Birmingham Post, Purnell felt it was time to move on. "I have been at the helm for the best part of 16 years," he said, "and have seen the company through the most fantastic and exciting changes: all for the better: which have far exceeded anyone's expectations."
Purnell plans to move to Norfolk and pursue a career as a freelance arts consultant.
The search for his successor began early this year.