He is the son of the famous Dynamo Kyiv and Soviet Union international footballer 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.
FC Obolon Kyiv dissolved itself in February 2013.
This biographical article related to a Ukrainian association football midfielder born in the 1980s is a stub.