Josef Ternström finished fifth in the individual cross-country race at the 1912 Olympics, helping the Swedish team to win a gold medal in team cross-country by the smallest of margins over the favored Finns, who had to settle for the silver medal. He was the Swedish individual cross-country champion in 1914 and took the individual cross-country silver at the 1915 Swedish championships. With the Gefle IF team, Ternström also won team cross-country silvers in 1914 and 1916 and team cross-country bronzes in 1915 and 1919 at the Swedish championships.