Boag was born in Portland, Oregon to Wallace B. and Evelyn G. Boag. He joined a professional dance team at age nine, later established his own dance school, and by the age of 19 had turned to comedy. He toured the world's stages in hotels, theaters and nightclubs. While appearing at the London Hippodrome in Starlight Roof, he brought a young 12-year-old girl on stage to help with his balloon act. The girl, a young Julie Andrews, astonished the audience with her voice and was kept in the show. In 1945, Boag signed a contract with Metro-Goldwyn-Mayer and appeared in films such as Without Love and Thrill of a Romance, albeit uncredited.
In the early 1950s, while appearing in revues in Australia, he met tenor Donald Novis. It was Novis who got Walt Disney to audition Wally for the Golden Horseshoe Revue, a 45-minute stage show which was written by its first pianist Charles LaVere and lyricist Tom Adair. Novis was the show's first tenor and was replaced by Fulton Burley when he retired in 1962. Both Wally and The Golden Horseshoe Revue were cited in The Guinness Book of World Records for having the greatest number of performances of any theatrical presentation. The show was often incorrectly introduced before a performance as the record holder of the longest running revue in the history of show business. The 10,000th performance of the Golden Horseshoe Revue was featured on NBC's The Wonderful World of Disney.
Boag's Pecos Bill/Traveling Salesman character was a fast-paced comedy routine featuring slapstick humor, squirt guns, a seemingly endless supply of broken teeth which he would spit out throughout the routine, and his signature balloon animals (Boagaloons).
In 1963, Julie Andrews once again performed with Boag on the Golden Horseshoe stage along with the Dapper Dans, at a special press-only event to promote the following year's release of Mary Poppins. Together, Andrews and Boag recreated their act of long ago and sang "By the Light of the Silvery Moon."
While Walt Disney was alive, he did everything he could to further Wally's career. Boag voiced Jose in "Walt Disney's Enchanted Tiki Room" and also wrote much of the script for the attraction, participating also in the development of "Haunted Mansion" in Disneyland.