Born in Stropkov, Kožlej began playing youth football for Tesla Stropkov and 1. FC Tatran Prešov. He is well known for his excellent goal-scoring ability and holds the all-time record among Slovak footballers.
He scored Larissa's first goal at 2007 Greek football Cup's final against Panathinaikos with a great header, when Larissa won 2–1 with the second goal scored by Henry Antchouet. He arguably spent his most productive seasons in terms of goals scored at Olympiakos Nicosia and has returned to this club to finish his career which occurred in the end of January 2010.