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Yaremchuk is a product of Karpaty Lviv and Dynamo Kyiv academies. On 6 September 2008, Yaremchuk made his debut for Dynamo in Ukrainian National Youth Competition. In his first match against FC Yunist Chernihiv he scored twice. That season he made 21 appearances and netted 10 goals.
In August 2017, Yaremchuk signed a four-year contract with Gent in the Belgian First Division A.
On 31 July 2021, Benfica announced the signing of Yaremchuk on a five-year deal for 17 million euros.[10][11] He made his debut for the club on 10 August, creating Benfica's second goal in the 2–0 home victory over Spartak Moscow in the third qualifying round of the UEFA Champions League.[12] Four days later, Yaremchuk made his debut in the Primeira Liga.