Daddio was an All-State performer at Meadville High School in Meadville, Pennsylvania. After a successful high school career, he moved to the University of Pittsburgh to play under coach Jock Sutherland. Daddio led the Panthers in receiving during the 1936 season. In each of his final two seasons at Pitt, 1937 and 1938, he was recognized as an All-American. During the 1937 Rose Bowl against the Washington Huskies, Daddio contributed significantly in the run game and returned an interception 71 yards in the fourth quarter to secure a victory for the Panthers. In 1953, Daddio retroactively received the Rose Bowl Player of the Game Award for the 1937 contest in Pasadena. In 1992, Daddio was inducted into the Rose Bowl Hall of Fame.
Daddio was selected by the Chicago Cardinals in the fifth round of the 1939 NFL Draft, rejoining former Pitt teammate Marshall "Biggie" Goldberg. He played two seasons with the Cardinals. His versatile play earned him second team All-Pro honors in 1942.
Daddio spent over two years with the United States Navy during World War II as a gunnery officer. For his service overseas, he was honored with the Bronze Star. Daddio's final of year of professional football came in 1946 as a player-coach with the Buffalo Bisons of the All-America Football Conference. He converted on all three extra points that he attempted that season.