The 24-year-old has signed a four-year deal at Elland Road, running until the summer of 2024.
The centre-back made his breakthrough with SV Eintracht Trier, before moving to hometown club 1. FC Kaiserslautern, with whom he also spent time with during his youth career.
After impressing in his 27 appearances in 2. Bundesliga during the 2016/17 campaign, Koch was snapped up by top-flight side SC Freiburg.
Over the past three seasons, Koch has made a total of 87 outings in all competitions for Freiburg scoring five goals.
During the 2019/20 campaign, he played 32 league games for Freiburg, helping them finish in eighth place in the Bundesliga.
His performances over recent seasons did not go unnoticed at international level, with Koch winning caps for Germany’s Under-21s, helping them reach the European Championship final in June 2019.
He was then handed his senior debut for Germany last October against Argentina, before winning his second cap against Belarus a month later.
Koch has been included in the latest Germany squad and could make further appearances in their upcoming games against Spain and Switzerland.