Concha began his career at the minor Malmö side Kulladals FF, before eventually signing for his home town giants, Malmö FF. In 2004, he moved to Stockholm and Djurgårdens IF after having been given playing time sparsely at Malmö FF. He quickly established himself as a starter for Djurgården and was part of their championship winning team of 2005, as well as Swedish cup golds 2004 and 2005. He played 76 games and scored two goals.
On 20 June 2007, it was announced that Concha would join the German football club VfL Bochum for the 2007–08 season. He signed a four-year deal with a team that had finished eighth the previous season. Concha left Bochum after the 2011–12 season.
On 30 July 2012, Malmö FF announced that they had signed Concha for two and a half years. He returned to play with the number 23 shirt, symbolizing his age when he left Malmö for the first time. Concha played his first match for the club on 16 August 2012 when he played 64 minutes in a friendly against Italian side Lazio. He played two league matches for Malmö FF for the 2012 season. Concha took over the number 2 shirt for the 2013 season. He was given a lot of field time in the beginning of what turned out to be a title winning season for the club, however when Miiko Albornoz returned from suspension, Concha lost his place in the starting eleven for the rest of the season. He played a total of seven league matches for the club during the 2013 season.