He began his football journey with Gwardia Białystok, joining the senior team at the beginning of the 1981–82 season.

In 1988, he moved from Mławianka Mława to Jagiellonia Białystok, where he played 14 matches in the top division and participated in the losing final of the 1988–89 Polish Cup.

[3] Since 2008, Kulesza has served as a sports advisor and proxy at Jagiellonia Białystok, later becoming a board member.

[5] The club also promoted many Polish national team players during this period, including Jacek Góralski, Bartosz Kwiecień, Taras Romanczuk, Karol Świderski, and Przemysław Frankowski.

On 18 August 2021, Kulesza became the 35th president of the Polish Football Association, defeating Marek Koźmiński in the second round of voting.