The Polish international has been speaking with club representatives for some time regarding fresh terms and has now signed an extended contract with the Elland Road club.
Klich has become the latest first-team player to commit his future to the club in recent months following the renewals of Luke Ayling, Liam Cooper, Stuart Dallas and Kalvin Phillips.
Klich initially joined the Whites in the summer of 2017 from Dutch side FC Twente and was the first signing made by director of football Victor Orta.
After making nine first-team appearances during his first season, Klich returned to Holland in January 2018 for a loan stint with FC Utrecht, helping them to a fifth-placed finish in the Eredivisie.
Upon returning to Leeds at the end of the campaign and following the appointment of Marcelo Bielsa as head coach in June 2018, Klich has started every league game for the club under the Argentine.
He made a blistering start to the 2018-19 campaign, scoring his first goal for Leeds against Stoke City on the opening day of the Championship season before going onto net a further two goals in August.
His fine form was rewarded with a recall to the Polish national team in September 2018 and he now has 22 caps to his name.
Fans' favourite Klich has made 75 appearances for Leeds in all competitions, scoring 12 goals.
Speaking earlier this week about his belief that Leeds have improved from last season, he said: “We are a better team.
“This season people think we did not start as well as last season but I think we have more points than at this stage last season. It is funny.
“I think we have grown as a team, basically the same players.
“Maybe it doesn’t look like we play better but on the pitch we can feel we’re better, more confident at the back.
“It gives us confidence for the attack.”