Yarmolenko is a graduate of the Chernihiv Youth Sports School "Yunist". He joined the Dynamo Kyiv Youth Academy at age of 13. However, he returned back to Chernihiv after a year being unable to meet physical requirements in training. Before his move to FC Dynamo Kyiv in 2007, he played for Yunist Chernihiv, Desna Chernihiv, Lokomotyv Kyiv, Vidradnyi Kyiv and again Yunist Chernihiv
In 2007, Yarmolenko signed a five-year contract with Ukrainian club Dynamo Kyiv, where he joined its second team, Dynamo-2, which plays in lower leagues, for a couple of seasons. The talented youngster was praised as the "new Sheva" by journalists, who noted his qualities of good physique, shot and especially his speed. The then vice-president of Dynamo, Yozhef Sabo, also praised the youngster, saying, "Yarmolenko has all the makings to become a top-level player."
On 11 August 2007 Yaromolenko represented Ukraine under-19 team in an away exhibition game against Japan, winning 1–0. He also participated in the 2008 UEFA European Under-19 Championship qualification.