He began studies at the University of Toronto in 1943, and studied engineering but left, in 1944, after failing his exams and joined the Canadian Infantry in 1944. He was honorably discharged in September 1945. After graduating from the University of Toronto with a Bachelor of Arts degree in Sociology in 1948, he worked variously in construction, at the Canadian National Exhibition, made an independent film with a classmate and acted in summerstock theatre. In 1951, he was working in the circulation department of the Toronto Star where he met his Future wife, Lila Melby. He also worked in the Avro Canada personnel department from 1953 until 1959 when he and most of the staff were laid off due to the cancellation of the Avro Arrow project. He then worked as an English and History Teacher at Burnhamthorpe Collegiate Institute in Etobicoke, Ontario.
in the late 1960s, he hosted CBC Radio show It's Debatable.
He joined the Ontario Educational Communications Authority (later TVOntario) in the early 1970s as a manager and, in 1974, was assisting with the establishment of its regional councils, when he was told OECA had acquired the broadcast rights to three Ingmar Bergman films and was asked if he had any ideas on how the station could air them in an educational context. Yost packaged the shows as Three Films in Search of God adding educational content in the form of interviews, introductions, and discussions thus creating the model for what became Saturday Night at the Movies, which became the channel's longest-running, and one of its most popular shows. Yost also developed Magic Shadows, which showed classic serials in half-hour early evening installments with introductions providing background and interesting details by Yost, the movie review show Rough Cuts, Talking Film and The Moviemakers. In 1979 he appeared in Ida Makes a Movie, the first of four television shorts that spawned The Kids of Degrassi Street in 1982.
His son, Graham Yost, is a Screenwriter whose most famous credit was the hit 1994 film Speed. Speed was the final movie Yost hosted before retiring from Saturday Night at the Movies in 1999.
In 1999, he was made a Member of the Order of Canada.
Elwy Yost wrote a mystery novel, White Shadows, which was published in 2003.
Yost recovered from "a serious operation" he had in 2005, according to his wife, Lila. He died in Vancouver, British Columbia on July 21, 2011, aged 86.
