Davis was born in Toronto, Ontario, Canada, to a Lawyer father and Psychologist mother. He began his acting career as a child in 1949, in radio drama and summer stock theatre. His cousins Murray and Donald Davis ran the Straw Hat Players in Ontario in the late 1940s and early 1950s, and rehearsed in the basement of Davis' house. When they needed a boy they gave william his first professional acting job. He went on from there to have a career as a boy actor on Canadian Broadcasting Corporation radio before his voice broke. In 1955 he enrolled in the University of Toronto to study philosophy, but actively pursued a career as an actor alongside Future actor Donald Sutherland. In 1959, he graduated from the University of Toronto with a Bachelor of Arts in philosophy. While at university he switched his attention from acting to directing and with his partner, Karl Jaffary, took over and ran the Straw Hat Players for four years.

In 1960 Davis went to England to train at LAMDA (The London Academy of Music and Dramatic Art). He worked in the UK for the next five years directing in repertory theatres and acting schools. He was artistic Director of the Dundee Repertory Theatre. His last position in the UK was as an assistant Director at The National Theatre of Great Britain under Laurence Olivier where he worked with Albert Finney, Maggie Smith, Derek Jacobi, and Ronald Pickup among others. He returned to Canada in 1965 to work at The National Theatre School of Canada and soon, at the age of 28, was appointed artistic Director of the English Acting Section. During this period he was also active as a freelance Director at major Canadian theatres. In 1971 he joined the newly formed Drama Department at Bishop's University in Lennoxvile, Quebec. While there he became the founding artistic Director of Festival Lennoxville, a professional summer theatre that ran for the next decade.

Despite being known for his smoking character, Davis quit smoking in the 1970s; when The X-Files started up, he was given a choice between herbal cigarettes and tobacco cigarettes. At first, he chose to use tobacco cigarettes, but switched to herbal because he was afraid of becoming addicted to them again. Davis used his notoriety on the show to assist the Canadian Cancer Society in its programs to combat smoking. In 2014, Davis donated his Investments that support fossil fuels to the David Suzuki Foundation in an effort to both ethically invest, and help fund work to fight climate change. Davis is a passionate advocate for action in response to climate change, believes it is a critical issue of our time and speaks on the subject often. Taking action on a personal level, Davis drives a Tesla powered by hydroelectricity.

Returning to Toronto in the late seventies Davis spent several years as a radio drama Director and on the faculty of Humber College. In demand as an acting Teacher during this period, he resumed acting after an absence of nearly twenty years. Davis earned a number of roles on stage and film before accepting the position of artistic Director of the Vancouver Playhouse Acting School, which required relocating with his wife and family. Davis writes in his memoir, "And so, in the fall of 1985, we hitched our second hand boat to our second hand car and drove across the country".

When asked about his belief in the paranormal at the London Film and Comic Con in 2010, Davis replied, "The onus is on you to prove the extraordinary ...I did a lot of research and saw where a lot of the arguments were wanting."

In 2011, Davis married Emmanuelle Herpin. He has two daughters, Melinda and Rebecca, from an earlier marriage. He also has two grandchildren.