Mornar began his career with Hajduk Split before going on to play for Eintracht Frankfurt, Sevilla FC, CD Ourense and Standard Liège, then moved to Anderlecht in the summer of 2001.
Mornar had enjoyed UEFA Champions League football in the months prior to his move to Fratton Park, scoring in a 1-1 draw at home to Bayern Munich.
The player was offered a new two-year contract by Anderlecht, but opted to move across the English channel to Portsmouth. He moved to the Premiership at the end of January 2004 for £500,000, signing a two-and-half-year deal.
Mornar made his Pompey debut in a goalless draw at home to Wolves, and looked lively. He then bagged his first and only goal in the next game against Spurs. A performance that earned Mornar the 'Swan d'Or', a celebrated Croatian sporting award.
The striker was a regular member of the Croatian national team in Euro 2004.
However, Mornar failed to recreate his previous form at Portsmouth. Seemingly out of the picture at Portsmouth, he was loaned to Stade Rennais FC for the 2004/05 season, with then Pompey manager Harry Redknapp saying he would allow Mornar to be sold upon his return. Although it appeared Mornar was in new boss Alain Perrin's plans for the 2005/06 campaign, he was thwarted by hamstring injuries throughout the season. Upon the return of Harry Redknapp as manager in December 2005 it looked as though Mornar's contract would be allowed to expire the next Summer. However, it transpired that there was a clause in his contract guaranteeing him a further year at the club should relegation be avoided and he remained a Portsmouth player, until September 2006 when his contract with the club was cancelled by mutual consent.