Živković began his professional career with Marsonia and Hrvatski Dragovoljac in his native country before spending six seasons with Bundesliga club Bayer Leverkusen.
Živković started his career at Sarajevo as a youth player, before being signed by Marsonia (from Slavonski Brod).
However, in December, a public fall-out with manager Harry Redknapp led to him being released, having played only 18 times for the club.
He was no longer in the team for the remaining two games Croatia played on the tournament before being eliminated — Italy and Mexico progressed from the group to the playoffs instead.
Boris was out of favour for the Zlatko Kranjčar's World Cup 2006 campaign but many defender injuries forced Slaven Bilić to give him a call for the Euro 2008 spring qualifying games.