Runje began his career at HNK Hajduk Split in 1996 but he left in 1998 because of heavy competition in the goalkeeper position, with Hajduk Split managers choosing Tonči Gabrić (then a national side 2nd choice goalkeeper) and eventually young prospect Stipe Pletikosa in front of Runje.
Between 1998 and 2001 he played for Belgian club Standard Liège before he went to Olympique Marseille. In France, he had two great years, but during the third season he lost his place to Fabien Barthez and returned to Standard Liège. There he won the best goalkeeper of the league award three times (in 1998–99, 2000–01, and 2005–06 seasons), before coming to Turkey to play for Beşiktaş in 2006. After finishing the season in which he was a regular first choice goalkeeper he left Beşiktaş to join Lens. Despite Runje's performances, Lens were relegated from Ligue 1 and speculations began that Runje might be leaving the French side, but in mid July, he decided to stay for next season.
Runje is married to his first love Tihana and they have a son Roko. Runje's younger brother Zlatko Runje is also a professional goalkeeper and is currently playing for Panthrakikos.
On November 15, 2006, he made his debut for the Croatian national football team in the Euro 2008 qualification match against Poland. He went on to have 2 more caps in the qualifications.