Tim Daggett competed for UCLA, helping them win the 1984 NCAA title, while placing second that year in individual all-around, and winning NCAA apparatus titles on rings, pommels, and parallel bars. He competed at the 1984 Olympics, winning the team gold medal and a bronze medal on pommel horse. Daggett continued to compete through 1988, trying to make that Olympic team, but injuries hampered his efforts in 1987-88. He was on US World Championship teams in 1983, 1985, and 1987, shattering his left leg in a bad landing on vault at the 1987 Worlds.
After retiring from competition, Daggett settled near his hometown of Springfield, Massachusetts with his wife, Deanne, an anesthesiologist. He ran a gymnastics facility in Agawam, Massachusetts and coached both boys and girls programs. Daggett has also spent many years as an expert commentator on gymnastics for NBC Television.