"I am very pleased with the transfer and Milivojevic is exactly the kind of player we were looking for," Anderlecht general manager Herman Van Holsbeeck told the club's website .
"He will join the team in a few days and be presented to the fans and the media shortly upon his arrival in Belgium," said Van Holsbeeck.
The 22-year old playmaker scored seven goals in 36 league games for former European champions Red Star, the debt-ridden Serbian club who have had to sell their top players.
He has made three international appearances but is yet to score for Serbia, who have only a slim chance of reaching next year's World Cup finals in Brazil.
Anderlecht have qualified for this season's Champions League group stage while Red Star face Ukrainian side Chornomorets Odessa in the Europa League third qualifying round.