Van Dyke was born on December 13, 1925, in West Plains, Missouri, to Hazel Victoria (née McCord; 1896 – 1992), a stenographer, and Loren Wayne "Cookie" Van Dyke (1898–1976), a salesman. He grew up in Danville, Illinois. He is the older brother of actor Jerry Van Dyke (1931–2018), who is best known for a role on the TV series Coach. Van Dyke has Dutch, English, Irish, and Scottish ancestry, with a family line that traces back to Mayflower passenger John Alden.
Van Dyke left high school in 1944, his senior year, intending to join the United States Army Air Forces for pilot training during World War II. Denied enlistment several times for being underweight, he was eventually accepted for service as a radio announcer before transferring to the Special Services and entertaining troops in the continental United States. He received his high school diploma in 2004 at the age of 78.