Selby, from Yorkshire, was the first winner of the women's snooker world title in 1976, when she beat Muriel Hazeldine 4-0 in the final, and took the title again as a 51-year-old in 1981.
In addition, she was world billiards champion on eight occasions between 1970 and 1978 and was awarded the MBE for services to sport in 2016.
A statement on the World Snooker Tour's official website said: "WST and the WPBSA thank Vera for her tremendous contribution to our sport and send condolences to her friends and family."
Selby was part of the BBC commentary team at the World Championship in 1982 and continued to play and coach well into her 80s.
Former world champion Shaun Murphy said on Twitter: "I didn't get to meet Vera Selby, but she was one of the pioneers of women's snooker and an early trailblazer for girls and women who followed. May she rest in peace."