Standing 6 feet 6 inches and weighing 267 pounds, Geesink made his mark in the Japanese-dominated sport of judo when he won the 1961 world championship. He was a two-time world champion by the start of the 1964 Olympics in Tokyo.

At the 1964 Games, Geesink competed in the open division, which was eliminated from Olympic competition following the 1984 Olympics. In his Olympic semifinal match against Theodore Boronovskis of Australia, Geesink won in just 12 seconds. In the finals, Geesink faced Akio Kaminaga of Japan, a favourite of the Tokyo crowd. Geesink put his opponent in a sash hold (kesa-gatame) to win the gold. Even more than the two world championships, Geesink's Olympic title had a major impact on international judo.

Geesink won his third world title in 1965 before retiring. In all, he won 13 European titles. He authored several books on judo and served on the International Olympic Committee.