Dudley was the Indians' lead radio announcer from 1948 until his dismissal by the club in January 1968. In 1969, Dudley broadcast for the expansion Seattle Pilots; when the club moved to Milwaukee and became the Brewers the following year, he did not join them. Dudley broadcast for a number of minor league teams in the 1970s before retiring. As an announcer, Dudley was known for his friendly, homespun style and his signature catchphrases: "Hello, baseball fans everywhere" (to start a broadcast), "The string is out" (describing a full count on a hitter), "A swing and a miss, he struck him out," "That ball is going...going...gone!" (to describe a home run), "Mighty close, mistah ump!" (describing an umpire call that he found questionable) and "So long and lots of good luck, you hear?" (signing off at the game's end – "you hear" sounded more like "ya he-ah?" in Dudley's vocal inflection).
Dudley was also a popular advertising pitchman in Cleveland, remembered primarily for his radio and television commercials for the Aluminum Siding Corporation (Garfield 1–2323) and Kahn's Hot Dogs – "the wien-ah the world awaited," in Dudley's unique parlance.