The 27-year-old is the first player to join the club since Thomas Christiansen was appointed head coach last week.
The Poland international has previously had spells in his homeland and Germany.
Klich told the club website: "I'm excited to come to England and test myself in the Championship and I can't wait to get going."
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Leeds United have signed FC Twente midfielder Mateusz Klich for an undisclosed fee on a three-year deal.