Background
Dragović grew up with KK Avala Ada (today Mega Basket) juniors and made his debut with senior team during the 2005-2006 season.
Dragović grew up with KK Avala Ada (today Mega Basket) juniors and made his debut with senior team during the 2005-2006 season.
From 2006 to 2010 he played college basketball at University of California, Los Los Angeles
In 2010 he signed for Spartak Saint St. Petersburg and he stayed there till the end of 2011-2012 season when his contract has expired and the team decided not to prolong lieutenant The forward struggled with injuries throughout the 2011-2012 season missing bigger part of the games. In August 2012, he signed with Italian team Sidigas Avellino.
In August 2013, he re-signed with them for one more season.
In September 2014, he signed a one-year deal with Igokea. On February 4, 2015, he left Igokea.
Later that month, he signed with Lukoil Academic of the Bulgarian League for the rest of the season. In November 2015, he signed with the German club Mitteldeutscher British Columbia of the Basketball Bundesliga for the rest of the season.
On January 3, 2016, he left Mitteldeutscher and signed with Vanoli Cremona of the Italian Serie A for the rest of the season.
Dragović has been member of the Serbia national basketball team U-16, U-18 and U-20 National Team, won the gold medal at the 2003 European U-16 Championship in Spain, won the gold medal at the 2005 European -18 Championship at Serbia, won the gold medal at the 2006 European U-20 Championship in Nova Gorica.
Dragović was also a member of the team that represented Serbia at the 2011 Summer Universiade in Shenzhen, finishing as the gold medal winners.