The 24-year old midfielder has officially transferred to Belgium's most famous club but Per club and league policy, terms of the transfer were not revealed.
Kljestan was delighted to be making the move to Europe but did not forget to thank Chivas for their assistance in making the deal possible.
"I'm very excited and proud to be joining a club like Anderlecht, and I wouldn't be there to sign with them today if I hadn't been for Chivas USA. I'm thankful to everybody at Chivas USA, from the coaching staff, management, all the fans, and teammates over the years that have helped me mold into the player I am today," said Kljestan. "I'm ready to take this exciting step in my career.
Chivas President and CEO Shawn Hunter added: "Since joining the team, Sacha has established himself as one of Chivas USA's all-time greats, not just for his accomplishments on the field, but for his dedication to his teammates and coaches, and passion for the club. We are thrilled that Sacha will have the opportunity to continue his development on an international stage, and look forward to seeing great things from this special player in the future."