 Kunyange zvazvo akasarudzwa nokuda kweYugoslavia squad pa1990 FIFA World Cup muItaly, Bokšić ane makore makumi maviri haana kutamba mumutambo, nemudzidzisi Ivica Osim achida vatambi vane ruzivo mumutambo. Kutevera kuzvitonga kweCroatia kubva kuYugoslavia Bokšić akave chikamu chakakosha chechikwata chenyika cheCroatia muma1990 pasi pemurairidzi Miroslav Blažević. Akatamba neCroatia pa 1996 European Championshipasi haana kubatanidzwa muchikwata che 1998 FIFA World Cup muFrance nekuda kwekukuvara kwaakatambura masvondo mashoma mutambo usati watanga. Bokšić pakupedzisira akaita World Cup yake yokutanga pazera remakore 32 pa2002 FIFA World Cup muJapan, achioneka mumitambo mitatu yeboka reboka, asati aenda pamudyandigere gore rimwe chete gare gare muna 2003. 