In his club career, Kosecki played for RKS URSUS, Gwardia Warsaw, Legia Warsaw, Galatasaray, CA Osasuna, Atlético Madrid, Nantes, Montpellier, and the Chicago Fire. He came to Major League Soccer in the Fire's inaugural season in 1998, joining fellow Polish internationals Peter Nowak and Jerzy Podbrozny. Kosecki proceeded to score the first goal in Fire's history in a 2-0 win over the Miami Fusion. He then helped the club to the MLS Cup and U.S. Open Cup double. Kosecki played two seasons in MLS, scoring 12 goals and 19 assists in league play, before retiring as a player.
For Poland, Kosecki was capped 69 times, scoring 19 goals between 1988 and 1995.