On 13 January 2020, Szymański travelled to Athens to pass his medicals and complete a move to AEK Athens.[5] The Polish midfielder will join the Greek club on an initial six-month loan, and AEK will maintain the right to buy him for a fee of €1,500,000.[6] One day later, the deal was made official and Szymański was presented by his new club.[7]
On 30 June 2020, Szymański signed a four-year contract with AEK after his transfer from Akhmat Grozny was made permanent.[8] The Greek club paid €1,300,000 for his services, while Akhmat will keep a resale rate of 15%.[9] Five days later, Szymanski scored his first goal for the club, sealing an emphatic 4–1 away win against Aris Thessaloniki.[10]
On 20 January 2021, he scored helping to a 2–0 home win against Apollon Smyrnis for the first leg of the Greek Cup round of 16.[11] On 15 February 2021, he sealed a dramatic 4–2 away win against AEL, after a low cross from Levi García.[12] The following week, Szymański scored a brace in a 2–2 home draw against Asteras Tripolis.[13]
On 5 December 2021, he was the only scorer in a vital 1–0 home win against rivals Panathinaikos.[14]
At the start of the 2022–23 season, the appointment of Matías Almeyda as the club's new coach helped Damian to revive his career, eventually receiving a call-up for the 2022 World Cup. He also became the team's second captain, behind Sergio Araujo. The Argentine coach managed to harness his athleticism and passion, making him a significant member of the team, thus attracting interest from various clubs including Standard Liège.[15]
On 20 April 2023, Szymański signed a new contract with AEK Athens, running until the summer of 2027.[16]
On 8 September 2021, Szymański scored his first goal, an equaliser in the injury time of the second half during a 1–1 2022 FIFA World Cup qualification draw against England.[18]