Yarmolenko’s parents, native Ukrainians, were originally from Smolianka village, Kulykivka Raion, Chernihiv Oblast. After their marriage, Valentyna and Mykola Yarmolenko moved to Leningrad (currently Saint Petersburg) where Andriy was born in 1989. In three years time (after the collapse of the Soviet Union), the family moved back to their native land and settled in the city of Chernihiv.

In December 2006, 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.”

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.

On 11 May 2008, Yarmolenko debuted for Dynamo’s first 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.

After the qualification on 10 October 2008, Yarmolenko was invited to the under-21 squad which played against the Netherlands. He later participated in qualification and finals of the 2011 UEFA European Under-21 Football Championship.

On 5 September 2009, in the 2010 FIFA World Cup qualification game against Andorra, Yarmolenko made his first senior appearance for Ukraine and scored in a 5–0 win. On 2 September 2011, in 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.

Yarmolenko scored a hat-trick on 15 November 2014, netting all of Ukraine’s goals in a 3–0 victory away to Luxembourg in UEFA Euro 2016 qualifying. In November 2015, Yarmolenko scored in both legs of Ukraine’s 3–1 play-off victory over Slovenia to qualify the nation for Euro 2016 final stages. Yarmolenko was subsequently included in Ukraine’s squad for Euro 2016, where he played in all three matches as Ukraine failed to score and finished bottom of the group.

In a match in October 2015, Yarmolenko committed a dangerous challenge which almost broke Shakhtar Donetsk player Taras Stepanenko’s leg. The two reconciled after the game and exchanged jerseys, but afterwards Yarmolenko threw Stepanenko’s shirt on the ground while he thanked the Dynamo fans. In the Shakhtar–Dynamo derby in April 2016, after the former won 3–0, Stepanenko stepped in front of the Dynamo fans kissing his Shakhtar badge. In a brawl that escalated, Yarmolenko kicked Stepanenko to the ground.

On 28 August 2017, Yarmolenko signed a four-year contract with Borussia Dortmund. On 10 September 2017, Yarmolenko made his debut for Dortmund as a substitute in the 79-minute against Freiburg. He then got his first start for Dortmund against Tottenham Hotspur in a Champions League fixture, where he scored Dortmund’s only goal in the 3–1 defeat.

On 11 July 2018, Yarmolenko signed for Premier League club West Ham United on a four-year contract for an undisclosed fee. He made his debut on 12 August in a 4–0 defeat by Liverpool. Making his first start for West Ham on 16 September, he scored his first two goals for the club in a 3–1 away win against Everton, the club’s first Premier League win of the 2018–19 season. Yarmolenko suffered an Achilles tear on 20 October 2018 in a 1–0 loss against Tottenham Hotspur, which ruled him out for the remainder of the season.

Yarmolenko returned to the first team squad for the start of the 2019–20 season. On 31 August 2019, he scored his first goal since his return from injury, doubling West Ham’s lead with a left-footed volley in a 2–0 win over Norwich City. He netted again in West Ham’s next home match in the Premier League, opening the scoring in their 2–0 defeat of Manchester United. In December 2019 he tore his adductor muscle and had still not returned to playing when football was suspended due to the COVID-19 pandemic in March 2020. He returned to training in May 2020 and on 1 July 2020, in his second appearance since 2019, he scored the winning goal against Chelsea in a 3-2 win.