Born in Lubin, Poland, Jagiełło started his career in his local club Zagłębie Lubin. When he was a teenager, he was targeted by clubs such as Juventus and AFC Ajax but decided to stay in Lubin.[1]
He made his debut for Zagłębie in a 2–1 defeat to Ruch Chorzów on 15 December 2013.[2]
On 31 January 2019, Jagiełło signed a 4.5-year contract with Italian club Genoa and was loaned back to Zagłębie for the remainder of the 2018–19 season.[3]
On 5 October 2020, he joined Serie B club Brescia on loan.[4] Jagiełło returned to Brescia on another season-long loan on 9 August 2021.[5]
On 17 January 2024, Jagiełło moved on loan to Spezia in Serie B.[6]
On 12 August 2024, Ekstraklasa club Lech Poznań announced they had reached an agreement with Genoa to sign Jagiełło.[7] The deal was formalised the following day, and he signed a three-year contract, with an option for another year.[8]