A son of farmers, Olavi Ojanperä did cross-country skiing and played pesäpallo (the Finnish version of baseball) as a youth and did not take up kayaking until 1948, after graduating from the University of Helsinki with a forestry degree and getting married. He was introduced to kayaking by his brother-in-law Olavi Puro, who was a well-known kayaker in Finland. Along with his brother-in-law, Ojanperä competed at the 1950 World Championships, where he failed to medal. In 1951 Ojanperä switched to Canadian canoes, which was an unusual discipline in Finland at the time. His biggest achievement came at the 1952 Olympics, when he won a surprising bronze medal in the C-1 1,000 m in front of a home crowd.
After the Olympics, Ojanperä won the C-1 1,000 m title, adding C-1 10K and relay silvers at the 1953 Nordic Championships. He competed with little success at the 1954 World Championships, but then retired from sports due to work constraints. In 1960, he made a comeback to compete at the 1960 Olympics, but was eliminated in the heats of the C-1 1,000 m. Domestically he won four Finnish titles – in the C-1 1,000 m and C-1 10K in 1951 and 1960. Outside of sports, Ojanperä worked with the Finnish wood processing company Helsingin Kyllästyslaitos Oy, which is now part of Versowood Group, and served as their CEO from 1977 until his retirement. He was also the chairman of Marjaniemen Melojat canoe club.
Finland