Career
He is the son of the famous Dynamo Kyiv and Soviet Union international football player Oleksandr Zavarov. Valeriy joined Arsenal Kyiv while his father was the head coach there. However, when Oleksandr was fired, Valeriy was also dismissed from the club, and joined Obolon Kyiv.
Football Club Obolon Kyiv dissolved itself in February 2013.