Having been around the world in various youth teams as a child, in March 2009, Kosecki moved to Legia Warsaw.[1]
He was loaned out several times at Legia; in July 2010, he was loaned to ŁKS Łódź,[2] and returned to Legia one year later;[3] in 2012 he was loaned to Lechia Gdańsk and in 2015, Kosecki was loaned to SV Sandhausen.
After a successful loan spell, on 6 August 2016, he joined Sandhausen permanently on a two-year contract.[4] He returned to Poland when on 22 June 2017 he signed a contract with Śląsk Wrocław.[5]
On 24 July 2018 he signed a contract with Turkish side Adana Demirspor,[6] where he reached the promotion play-off finals, with the team losing out to Hatayspor, although he missed the finals themselves due to injury.[7] After only 6 appearances in the 2020-21 season he left in February 2021 after terminating his contract by mutual consent.[8] In February 2021, he signed a deal with the Polish Ekstraklasa side Cracovia.[9]
On 1 February 2022, he signed a contract with II liga club Motor Lublin until the end of the 2021–22 season, with an option to extend for another season.[10]