Veselinović progressed through the youth system of Partizan as one of the club's most promising prospects, breaking into the first-team squad under manager Lothar Matthäus in the second half of the 2002–03 season.
[1] He was later assigned to their affiliated club Teleoptik on dual registration, racking up an impressive goals-to-games ratio in the Serbian League Belgrade.
After returning to Partizan in the 2005–06 season, Veselinović again struggled to receive more playing time, but continued to score regularly for Teleoptik in the Serbian League Belgrade.
After spending over a year without competitive football, Veselinović signed with Serbian SuperLiga side Spartak Subotica in June 2012.
[2] Veselinović played for the Serbia national under-21 team in their opener of the 2009 UEFA European Under-21 Championship qualification, coming on as a substitute in a 1–1 home draw with Latvia.