The appointment sees Makelele take on his second senior role after previously managing Bastia, but the Frenchman has revealed that he has been grateful for the opportunity to work at the Premier League side.
The 44-year-old told the club's official website: "I've really enjoyed my time at Swansea, especially helping the club secure its Premier League status last season.
"I'd like to thank the owners, chairman and the manager for giving me the opportunity. The experience has given me a lot of positives to help me in my managerial career in the future – and I hope I've been able to give something back to the club along the way.
"It's a wonderful football club; a real family club that's been a pleasure to serve. I'd like to thank everyone for the welcome and help I've received in Swansea from the backroom staff to the fans."
Makelele makes the switch to Eupen with the club currently sitting bottom of the top-flight table.