The 27-year-old central midfielder has signed a three-year deal at Elland Road and becomes their first signing under new head coach Thomas Christiansen
Klich was at FC Twente for a season after spells in Germany with Wolfsburg and Kaiserslautern. He also has 10 caps for Poland, scoring one goal.
“I am very happy to have signed for such a huge club and I’m looking forward to playing in the famous white shirt,” Klich told the official club website.
“I’m excited to come to England and test myself in the Championship and I can’t wait to get going.
“The team came close to promotion last season so hopefully we can go one better and I’m looking forward to meeting my new team mates next week and getting started.”