Sterner made his hockey debut at 15 when he was accepted onto a second division club where he made a name for himself with his speed and scoring ability. On 12 November 1959, he made his international debut with Tre Kronor in a friendly match against Czechoslovakia's team. He scored his first goal in that game, which Tre Kronor won 11–3. He was the team's youngest player of all time. Through the late 1950s and early 1960s, he was one of Sweden's most popular players. He is also credited with inventing the "stick to skate to stick" maneuver. At the 1962 World Ice Hockey Championships, Sterner scored what he described as his most memorable goal when he scored the 3–0 goal against Team Canada. His team won the game 5–3 and took the gold medal. At the 1963 World Championship, he scored a hat trick against Canada in a 4–1 win. After the game, he and teammate Sven "Tumba" Johansson met King Gustaf VI Adolf and received a royal congratulations. His first Olympics came in 1960 in Squaw Valley. The team did not earn a medal, but from that point on he was a dominating centre in international play. By 1963, the New York Rangers had taken interest, and in October, Sterner made the trip for training camp. The parties signed a five-game tryout agreement, but Sterner declined to play that season in order to conserve his amateur status for the 1964 Winter Olympics. The team won a silver medal. Sterner arrived for training camp in 1964 and displayed excellent skills. However, the NHL, unlike the International Ice Hockey Federation, permitted hitting and physical play on any point of the ice; international players were not allowed to hit in the offensive zone. Allowing him time to adjust to the North American game, the Rangers offered him a start with the St. Paul Rangers of the Central League, which he accepted. After two months, he adapted and earned a promotion to the Baltimore Clippers of the American Hockey League. Finally, on 27 January 1965, he joined the Rangers in a game against the Boston Bruins, becoming the first European to play in the NHL. Ultimately, Sterner played only four games in the NHL, and he did not register a point. He had been reluctant to play physically or to instigate physical play. He was sent back down to the AHL, and it soon became clear that he was not going to return to the NHL. As much as his skills carried him through games in the AHL, he simply did not have the training to play 60-minute games with full contact. In 1969, the IIHF adopted the same body-checking rules as the NHL, and four years later, Börje Salming joined the Toronto Maple Leafs, ending up playing 17 years in the NHL.
Personal life
Sterner, his wife Pia, and their family currently live on a farm near Karlstad, where they keep four horses. He nicknames his horses after former teammates and friends; when one of the horses smashed his nose, he nicknamed it Alexander Ragulin.