On 16 January 1986, Medvedtsev achieved the feat of winning his World Cup debut.

At the 1988 Olympics in Calgary, Medvedtsev, competing for the USSR, won two silver medals in the 10 km sprint and the 20 km individual, and also gold medal in the relay.

At the 1992 Olympics in Albertville he won a silver medal in the relay competition for the Unified Team.

He also has one gold medal from the 10 km from 1986 in Oslo (Holmenkollen Ski Festival biathlon).

[citation needed] All results are sourced from the International Biathlon Union.