The 32-year-old was even given a guard of honor on Wednesday after the game against West Ham.
Klich's teammates wore t-shirts with a photo of the midfielder smoking a cigar following Leeds' promotion to the Premier League in 2020.
Klich initially signed with Leeds in 2017, completing a $1.8m (£1.5m) move from FC Twente in Holland.
He went on to play 92 consecutive matches under ex-manager Marcelo Bielsa in the Championship and has appeared in all but eight of Leeds' 76 matches in England's top flight between now and 2020.
Through his five years in England, Klich has made a total of 170 league appearances for the Whites.
This season, the Pole's appeared in 11 league matches and has only come off the bench.
D.C. United have the likes of several European players on its squad, including ex-Liverpool and Aston Villa striker Christian Benteke, former Liverpool academy player Victor Pálsson and ex-Manchester United wonderboy Ravel Morrison, though the latter is believed to be on the move from America's capital.
D.C. United ended last season on a sour note, as the bottom seed of the Eastern Conference. The team has also missed the Audi MLS Cup Playoffs for the last three seasons.
Other than Twente and Leeds, Klich has played in Germany for Wolfsburg and Kaiserslautern, as well as PEC Zwolle in Holland after breaking through at Polish club Cracovia.