Borzov started his athletics career in 1968. His first major achievement was winning the sprint-double at the 1971 European Championships in Helsinki, though he had already won the 100 m in 1969.
At the Olympics in Munich, two of the American sprinters (Eddie Hart and Reynaud Robinson) were eliminated because their coach had not announced the correct starting time of the heats. After Borzov won the final with relative ease, the Americans swore they would beat Borzov in the 200 m.
However, with all three Americans in the final this time, Borzov beat everybody again, displaying his excellent form. The Americans finally got their sprint gold, as they won the relay event, with Borzov's Soviet team taking second place.
Between Munich and the next Olympics in 1976, Borzov spent more time on his studies, though he did win his third successive 100 m title at the European Championships in 1974. False rumours of a planned assissination attempt on Borzov and his possible defection surrounded his return after an injury at the Olympics. He finished the 100 m race in third position, winning his fourth Olympic medal. In the 4 x 100 m, he won his fifth, another bronze.
A persisting injury meant Borzov had to abandon his hopes of a third Olympics, and he ended his career in 1979, after he had married four-fold Olympic gymnastics champion Lyudmila Turishcheva.
From 1991 to 1998, Borzov was president of the Ukrainian Olympic Committee, has been a member of the International Olympic Committee since 1994 and is Ukrainian minister of Youth and Sport.