Edminston discovered early in his life he could mimic people's voices, impressing his family with imitations of Lionel Barrymore. He went to the Pasadena Playhouse to study acting after World War II. He was discovered by animation producer Walter Lantz, which got him his first role in Time for Beany. After this, he hosted The Walker Edminston Show over the next two decades, a children's show which featured puppet characters of his own creation. Most of his work came with Sid and Marty Kroft on Saturday morning television series, including The Bugaloos, H.R. Puffnstuf, and Sigmund and the Sea Monsters. He also gave his voice to Inferno in the television series Transformers. He is known for serving twenty years as the characters Tom Riley and Bart Rathbone on Adventures in Odyssey. Edminston had numerous guest roles in television, including on Maverick, Star Trek, Get Smart, The Dukes of Hazzard, and Gunsmoke. He also supplied voices in all five Planet of the Apes films.