Klich was a regular in Twente's starting line-up last season, helping them finish seventh in the Eredivisie table and chipping in with eight goals and six assists.
Klich joins the likes of Eunan O'Kane, Ronaldo Vieira, Kalvin Phillips and Liam Bridcutt in the Leeds midfield ranks, and he will be looking to nail down a first-team place ahead of the new Championship season.
Leeds United have snapped up Polish global Mateusz Klich.
Ronaldo Vieira, the club's talented teenage midfielder, has agreed a long-term contract at Elland Road.
Burnley, who are also being linked with Hull City's Andrew Robertson, are keen on taking Taylor and would meet his wage demands, but want to secure a private deal with Leeds.
Formerly of Cracovia, Wolfsburg and PEC Zwolle, Klich will now be hoping to make a considerable impact in West Yorkshire having become the first signing under new boss Christiansen.
Asked for his first impressions of Leeds and Elland Road, Klich beamed: "I am really happy to sign here".
Leeds turned winger Hadi Sacko's season-long loan from Sporting Lisbon into a permanent move earlier this month.