Career
Bundesliga club RB Leipzig. The defender moved during the 2002-2003 season from the youth team of the VfB Stuttgart to the amateur team of Borussia Mönchengladbach. In 2005, he got a professional contract.
Because of the injuries of both Filip Daems and the national defender Marcell Jansen he became a regular player in the autumn of 2006 in the Bundesliga.
In the first half of the 2007-2008 season, Compper played only three games for Borussia Mönchengladbach. Due to this, he transferred to TSG 1899 Hoffenheim in January 2008.
In January 2013, he transferred to Fiorentina. On 2 August 2014 he signed a deal with 2.
Bundesliga side RB Leipzig.
He received his sole international cap for Germany on 19 November 2008, against England making him the first Hoffenheim player to be capped by Germany.