Bokšić was born in Makarska and started his career at the club Zmaj from his birthplace. Soon he left for the Croatian Club Hajduk Splitin 1987 , where he ended up in the first team. At this club, he won his first prize: the Yugoslav Supercup in 1987, in 1991 he won this award one more time. During the final of 1991, he made the only goal of the match. He played 174 games for Hajduk sixty goals.
In the season 1991/92 left Bokšić at Hajduk. He went to France to play for AS Cannes. Because of many injuries, he played only one game, after which he went toOlympique Marseille. He won the French League Championship that year and the Champions League and was also top scorer of the competition with 23 goals. In 1993 he finished in second place in the election, European Footballer of the year Roberto Baggio behind.
After his time at Marseille left Bokšić to Italy. He began his first stint with Lazio, which would last until 1996 . After this period he played one year for Juventus, where he won the Dutch title. After this season he returned to Lazio, where he twice the Italian Cup, the League title and won the UEFA Cup winners ' Cup .
On 4 June 2012 , it was announced that Bokšić along with other Croatian former players the assistants team of the Croatian national coach Igor Štimac would form. After Croatia, also finished the course Štimac left by Bokšić as Assistant trainer at the official sponsor.
-  Olympique Marseille