A native of Goldsboro, North Carolina, Kasell was a student of drama in high school, where one of his mentors was Andy Griffith, then a high school drama instructor. Although Griffith urged Kasell to pursue a career in theatre, Kasell took to radio at an early age as well. During his time at the University of North Carolina at Chapel Hill, he helped launch local radio station WUNC with fellow student Charles Kuralt.
He worked as an announcer and deejay at a radio station in Goldsboro before moving to the Washington, DC area in 1965. He advanced to the position of news director at WAVA in Arlington, Virginia before joining National Public Radio's staff as a news announcer in 1975. He has been the news announcer for NPR's Morning Edition for much of that time and continues to hold that post.
In 1998, Kasell was finally able to join the phenomenon of radio game shows which attracted him to the genre in his youth when NPR launched it's weekly news quiz, Wait Wait... Don't Tell Me, with Kasell as official judge and scorekeeper. The prize that Wait Wait... offers to its listener contestants is a recording of Kasell's voice for their personal telephone answering machines.