The 32-year-old made his final appearance for the Whites as a substitute in the 2-2 Premier League draw at home against West Ham United on Wednesday night.
Klich was given a guard of honour on the Elland Road pitch after the game by his teammates, who wore t-shirt with the midfielder's face on the front and his name and number on the back.
The Poland international was visibly upset as he walked off the pitch, with his five-year spell at the club coming to an end.
Klich is now set to make the switch to the MLS, with The Athletic reporting that DC United have won the race for his signature.
A statement from Leeds' official website read: "Leeds United can today announce Mateusz Klich will leave the club, pending an offer from Major League Soccer.
"Now 32, Klich has found playing time limited this season, with all 13 of his appearances coming from the bench. He now departs Leeds with the best wishes of the club, with a move the MLS set to follow.
"Everyone at Leeds United would like to thank Mateusz for his efforts during his time at the club, his contribution is truly unforgettable.
"He has acted with the upmost professionalism throughout his time at Elland Road and will always be respected by everyone at the club.
"Mateusz leaves Leeds United as a champion and will always be welcome at Elland Road. We wish him all the best as he starts a new chapter in the USA."
Speaking about Klich's decision to leave the club at a post-match press conference, head coach Jesse Marsch said: "There were a lot of different discussions, Klichy is being provided with an opportunity that he thought was a little bit more long standing and provided stability for his family, and an opportunity to try something new.
"So him and I had discussions over the last three, four weeks that were often unsure about what the final decision should be. And by the way, it's not finalised quite yet. I mean, it looks like it's going in that direction.
"We're all wearing t-shirts and I understand that that makes everybody believe it's finalised. But even at this moment, I knew in a match like this one we needed more courage on the pitch that Klichy was the right guy to have because this is who he is.
"This is how he lives life and plays football. It won't be easy to lose him and I think if we were to say between he and I we're not absolutely sure that it's the right decision, but I certainly wish him the best."
Klich joined Leeds from Dutch outfit FC Twente in the summer of 2017 and became the club's first signing under director of football Victor Orta.
The midfielder scored the first goal of the Marcelo Bielsa era back in August 2018 and excelled under the Argentine boss, establishing himself as a key player in Leeds' Championship title-winning side in 2019-20.
Klich went on to record 24 goals and 21 assists in 194 appearances for the Whites across all competitions, including 12 goal contributions in 81 Premier League games.