Vyacheslav Vedenin was one of the best long distance cross-country skiers in the late 1960s and early 70s. Vedenin made his first international appearance at the 1966 World Championships, where he was sixth at 50 km and eighth in the 15 km. At the 1968 Olympics, Vedenin won the only medal among Soviet male skiers by finishing second in the 50 km. In Grenoble he was also fourth in the relay and fourteenth at 30 km. At the 1970 World Championships Vedenin won two golds, in the 30 km and relay, and one silver over 50 km.
At the 1972 Olympics, Vedenin first won gold in the 30 km, becoming the first Soviet male skier to win an individual Olympic title, and then placed third behind Norwegians Pål Tyldum and Magne Myrmo in the 50 km. Three days after his bronze in the 50 km, Vedenin skied the anchor leg for the Soviets in the relay. After three legs, the Norwegians had a comfortable lead, over a minute ahead of the Soviet Union, but Vedenin managed to reduce the gap to only 30 seconds after 5 km, and he continued to increase his pace, catching Norwegian anchor Johs Harviken only 100 metres from the line. While trying to counterattack, Harviken fell, and Vedenin, with the fastest leg of the competition, won an Olympic relay gold for the Soviet Union, ten seconds ahead of Norway.
In 1972 Vedenin also won the Vasaloppet and continued to ski a few more seasons until an injury put an end to his sporting career. Domestically Vedenin won 13 Soviet titles – one at 15 km (1969), four at 50 km (1967-69, 1972), two at 70 km (1969, 1970) and six in the relay (1966, 1968-70, 1972, 1973). After his competitive career Vedenin worked as a cross-country skiing coach with Dynamo Moskva. Every year since 1989, races named in his honor are held in Dubna, near his birthplace.