Alexander Jeremejeff was born on 12 October 1993 in Kungsbacka, Sweden, and began his football career in the youth teams of Tölö and then Örgryte, where he made his first professional steps.

In 2013, he transferred to Qviding, scoring 14 goals and one assist in 21 appearances, before continuing his career with Häcken for the 2014–15 and 2015–16 seasons, where in 51 appearances he scored 17 goals and served up nine assists while also winning the Swedish Cup in the 2015–16 season.

In the summer of 2016, he moved to Malmö, where he registered 57 appearances, 14 goals and 13 assists, winning two Swedish championships. In July 2018, he returned to Häcken, making 34 appearances, scoring 17 goals and providing 11 assists in a busy season.

In August 2019, he moved to Dynamo Dresden, where he played in 24 games, scoring four times and providing three assists. In August 2020, he was loaned to Twente, where he played in 10 games and scored once. His loan ended in January 2021, and the Swedish striker left Dynamo Dresden and returned to Häcken once again.

Jeremejeff was the top scorer in the Swedish league in the 2021-22 season with 22 goals, leading Häcken to the Swedish league title in the 2022 season. In total, in his third term at the club, he recorded 63 appearances, 40 goals and six assists.

In January 2023, he moved to Greece with Panathinaikos, who immediately loaned him to Levadiakos until the end of the season, where he played in 10 matches and scored one goal and contribured two assists. After the end of the loan, the Swedish striker returned to Panathinaikos and in two and a half seasons he recorded 60 appearances, 16 goals and one assist in all competitions, while also winning the Greek Cup in the 2024-25 season.