The 31-year-old, who has been capped by Slovenia, has also played for Udinese, Perugia and Anorthosis Famagusta.
He told the Killie website: "The opportunity to join Kilmarnock is a really exciting one and I’ve heard good things about the club and Scottish football. I know Massimo (Donati) from my time in Italy and I can’t wait to get started here.”