The 1-1 draw with West Ham was Klich's last game for the Whites ahead of a January move to the United States, with Wayne Rooney's DC United reported to be his next club.
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Klich is a popular figure in Yorkshire after five years at the club and manager Jesse Marsch ensured the player received a fitting send off.
The Poland international came off the bench in the 60th minute and broke down in tears at full-time.
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Marsch and his Leeds players donned t-shirts paying tribute to the 32-year-old midfielder as Elland Road said goodbye.
Taking to Instagram, Klich wrote an open letter to the club and its supporters, expressing his deepest affection.
He finished by explaining why his time in Leeds must come to an end.
Klich wrote: "I wish I could stay, but I have never enjoyed being on the bench and I want to play as much as I can in the coming years and that is why I am closing this chapter, but I will never forget my time in Yorkshire."
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Klich's deal at Leeds runs until 2024 but the Pole was not willing to accept his new role as a substitute under Marsch - and the contract offer from America was too good to turn down.
"This was not a black-and-white decision," Marsch said.
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"This was a lot of different discussions, Klichy being provided with an opportunity that he thought was a little bit more long-standing and provided stability for his family and try something new.
"It won't be easy to lose him and if we were to say that between he and I, we are not absolutely sure it's the right decision, but I certainly wish the best for him."