He first gained recognition for portraying Giovanni delle Bande Nere in the period drama The Profession of Arms (2001), and later became better known for his leading role as St. John in Mel Gibson's The Passion of the Christ (2004).
Jivkov also appeared in numerous Italian films and television shows, including The Good War (2002), Eyes of Crystal (2004), The Inquiry (2006), The Lark Farm (2007), David's Birthday, Barbarossa (both 2009), The Invisible Boy (2014) and Lucania (2019).
In 2003, Jivkov starred in Mel Gibson's The Passion of the Christ alongside Jim Caviezel and Monica Bellucci.
The film achieved success at the box office, grossing $612 million worldwide.
Tributes were paid by his friends and colleagues Mel Gibson, Maria Grazia Cucinotta and Dessy Tenekedjieva, among others.