He started his professional career in 1999 with his hometown club Mladost. He moved to Medvescak for one season and returned to Mladost in 2001. He played around 250 games during a six year span in which he scored 150 goals. With Mladost he won the Croatian Championship and the Croatian Cup twice and finished in the third place in the Final Four of the Champions League.
In 2007 he signed for one season for another Croatian club, Sibenik NCP . He played 45 games scoring around 30 goals and finished third in the Croatian League. A year later he moved to Jadran Herceg Novi in Montenegro, with whom he won the Montenegrin League, and finished runners up in the Cup and the Adriatic League.
In 2009 he earned his first contract in Italy with Brescia Leonessa. He played around 50 games for Brescia in the process of which he averaged more than 1 goal every game. During this season Brescia came third in the Italian League and Cup and were eliminated in the semi-final of the LEN Cup.
In 2010 he returned to Croatia where he played three seasons for Primorje ESB, during which they always placed as runners up in the Croatian League, won the Croatian Cup and the Adriatic League in 2013 and placed second in the Final Four of the Champions League in 2012.
Seasons 2013-2014 and 2014-2015 saw Marko in the colours of Como Nuoto in Italy. He played around 60 games for Como scoring more than 80 goals in the process.
In 2015 he joined his current team, BPM Sport Management, with whom he placed third in the Italian A 1 and in the Italian Cup.
Marko is also a former Croatian National Team Player. He earned his first cap in 2004 and played 20 times for Croatia netting 15 goals. During this period Croatia ended fourth in the World League in 2005, in the World Cup in 2006 and in the Mediterranean Games in 2006.
In 2010 Marko Jelaca was called up by the National Team of Georgia with whom he qualified for the 2014 and 2016 European Championships. He has played around 50 games for Georgia for whom he has averaged 2 goals per game.