Tumba was named his country's best-ever hockey player and later became a golf pioneer in his native Sweden and the former Soviet Union. Tumba was inducted into the International Hockey Hall of Fame in 1997. A three-sport star, Tumba also represented Sweden in soccer and golf in international competition. In the early 1950s, he played for the national soccer side and became a Swedish champion while playing with Djurgarden in 1959. Starting in 1951, Tumba also played hockey for Djurgarden and won eight Swedish championships and three goal-scoring titles. He represented Sweden at 14 world championships and four Winter Olympics, and was named best forward at the 1957 and 1962 worlds, and top goalscorer at the 1964 Winter Olympics when Sweden's amateurs finished second behind the Soviet Union's state professionals.
In 1997, he was inducted into the International Hockey Hall of Fame and in 1999 he was named Sweden's best-ever player, beating out prominent players such as former NHL MVP Peter Forsberg and Mats Sundin, both Olympic champions.
In 1957, he helped Sweden win the world championship title ahead of the Soviet Union before an outdoor crowd of more than 50,000 at Lenin Stadium. The organizers did not have the Swedish national anthem ready for the post-game ceremony, so the Swedish players instead sang Sweden's most famous schnapps song that was broadcast over the PA system. "Hockey was my whole life, that's what my heart was in," he told Swedish Radio in an interview during the summer of 2011. According to the association, Tumba in 1958 became one of the first European players to attend an NHL training camp, but never signed a contract with the Boston Bruins and returned to Sweden. After retiring from hockey, Tumba turned his attention to playing golf, though he also took on course design and became an ambassador for the game. In the early 1960s he took his first swing on Sweden's oldest golf course on Lidingo island outside Stockholm, putting his ball on the green before two-putting for par on the first hole. He was hooked on the game thereafter. "Golf is not a sport, it's a disease," he told Swedish media after discovering his newfound love for the sport. As a golf pro, he founded the Scandinavian Enterprise Open, now the Nordea Masters and one of the best attended European Tour events. During the Swedish Golf Federation's centennial in 2004, Tumba received an award as the most influential individual in Swedish golf ahead of Annika Sorenstam among others.
During his final years, Tumba devoted much of his time to the Sven Tumba Education Fund, a global project using sport to help children develop in interest in reading and writing, teamwork, sharing and self respect. In 2006, the fund was endorsed by soccer's world governing body FIFA and its president Sepp Blatter.