In the 1960s and 1970s Leonid Osipov represented the Soviet Union’s dominant water polo team that won medals at the Olympics and at the both the European and World Championships. Osipov made his first appearance at the Olympics at the 1964 Games in Tokyo where the team won bronze. Two years later he was part of the team that won gold at the European Water Polo Championships in Utrecht. He returned to the Olympics in 1968, wining silver at the Mexico City Games in a closely-fought contest against Yugoslavia.
In 1970 the Soviet team defended their European title when they won gold in Barcelona, making the team one of the favourites ahead of the 1972 München Olympics. In a tight final group, Hungary and the Soviet Union tied with three wins and two ties, as they tied in their head-on match, 3-3, with the Soviet Union winning their first water polo gold medal by goal differential. Osipov won his final international medal three years later with silver at the World Championships in Belgrade, with the Hungarian team taking home gold. After his playing career Osipov worked as a coach for the Armed Forces team before being elected as a member of the FINA technical committee.