Bobrov was born in Morshansk on 1 December 1922 and moved to Sestroretsk in 1925, along with his parents and two siblings. He first started to skate at the age of 5, and played bandy from a young age. He left school when he was 13 in order to work in a factory.
Playing career
After serving in the Soviet Army during World War II, he was invited to play football for the Army club CSKA Moscow in 1945. That same year, he joined Dynamo Moscow on their 1945 tour of the United Kingdom; he scored 6 of the 19 their goals, and it was on this tour that he saw artificial ice for the first time. Playing until 1953 for CSKA, VVS, and Spartak, he would go on to win the Soviet Championship three times, scoring 97 goals in only 116 games. Bobrov led the country in goals in 1945 with 24 and 1947 with 14. Chronic knee problems led to him having surgeries in 1947, 1950, 1952, and 1953, to fix the issue, though it never was resolved. He was capped three times for the Soviet Union national team representing them in the 1952 Summer Olympics. He scored five goals in total, including a hat trick against Yugoslavia, though the Soviets lost that match and failed to medal. He was also part of the CDKA team that was disbanded due to this loss, and transferred to Spartak Moscow for his final season of football. Bobrov began playing hockey for CSKA a year after his football start, in 1946. However, due to a knee injury sustained during the football season, he missed the first season. His playing career in this sport lasted until 1957, with the years between 1950 and 1953 spent with VVS. Although football was Bobrov's first sport, his success in ice hockey was even greater. In 1950, a plane crash almost killed the entire VVS Moscow team. Bobrov survived the crash as he overslept and travelled by rail. In the Soviet Championship, which his teams won seven times, Vsevolod scored 254 goals in only 130 games. He played for the Soviet national team in the 1956 Winter Olympics, becoming one of the few athletes to participate in both the Summer and Winter games. Bobrov proceeded to lead his country to the gold medal, and also won the World Championship in 1954 and 1956. Overall, he scored 89 goals in 59 games for his country. In Russian ice hockey, his name was given to an exclusive list of players, the Bobrov Club, who scored over 250 goals during their career. Bobrov, who served as a player-coach in both sports during his time with VVS, would go on to coach various teams after retiring as a player in both football and ice hockey. In the latter, he coached the USSR in the 1972 Summit Series and then led them to the World Championship in 1974 and 1975.