A goalie, Kjell Svensson played most of his career from 1954-69 with Södertälje SK, except for short spells with Tabergs SK (1959-60) and AIK (1960-62). With Södertälje, Svensson won his only Swedish title in 1956, but was selected to the Swedish Championship all-star teams in 1960-61 and 1963-64. Svensson was also the top goalie of Swedish national team in the 1960s, being capped 148 times and playing at two Olympic and five World Championship tournaments. Svensson won Olympic silver in 1964, was a World Champion in 1962 and won silvers at the 1963 and 1967 and bronze at the 1965 World Championships. He was also a European champion in 1962, while taking silvers at the 1963, 1964 and 1967 and bronze at the 1960, 1961 and 1965 European Championships. Because of those accomplishments, Svensson was awarded the Stora Grabbars Märke (Big Boys’ Badge) #60 in ice hockey.
After finishing his sports career, Svensson worked as an ice hockey coach for awhile, coaching Södertälje SK in 1972 and 1975-78 and also coaching the Swedish national ice hockey team in 1973-74. After his coaching career, Svensson had a successful career with the Swedish truck manufacturer Scania, where he eventually rose to be Senior Vice-President of truck manufacturing. Svensson was also a member of the board of directors of the Swedish Ice Hockey Association in 1986, but resigned after six months because of his career with Scania.