Yarmolenko is generally a pupil of the Chernihiv youth system. He joined Dynamo Kyiv Youth Academy at 13. However, he returned to Chernihiv after a year, unable to endure the physical demands of training. At the start of his professional career he played at local clubs Polissia and Desna before joining Dynamo.
In December 2006 Yarmolenko signed a five-year contract with Ukrainian giants, Dynamo Kyiv, where he was placed in its second team Dynamo-2 that plays in lower leagues for 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. Then-vice-president of Dynamo, Yozhef Sabo, also praised the youngster, saying that "[Yarmolenko] has all the makings to become a top-level player."
On 11 May 2008 Yarmolenko debuted for Dynamo's main team in an away match against Vorskla Poltava and scored the winning goal in Kyiv's 1–2 victory. He scored 7 goals in 21 games in his first season and 11 in 19 in his second. He is now regularly used as a left or centre forward.
On 2 September 2011 when Ukraine had an international friendly against Uruguay in Kharkiv, Yarmolenko set a national team record by scoring 14 seconds into the match, the fastest time in which a Ukraine national team player has scored a goal.