Anderlecht, founded in 1908 and one of Belgium's best known teams with a string of European titles in the 1970s, had been owned by a group of investors headed by the Vanden Stock family.
While the top-flight club did not say how much Coucke paid for Anderlecht, local media had reported an asking price of up to 100 million euros (£88.6 million).
"It pleases me to look back at the time when my father and my family owned the club, but it is time to pass on the baton, so RSC Anderlecht can always remain RSC Anderlecht," Anderlecht president Roger Vanden Stock said in a statement.
Coucke founded over-the-counter medicines group Omega Pharma, which he sold to U.S. company Perrigo in late 2014 for 3.6 billion euros
He also owns Belgian club KV Oostende and previously had a stake in France's Lille and was a title sponsor for cycling team Quick Step.
Les Mauves, as Anderlecht are known because of their purple and white club colours, have been knocked out of Europe this season after finishing bottom of their Champions League group.
They have also had a difficult domestic league campaign, losing 5-0 to perennial adversaries Club Bruges on Sunday. They are in third place, 13 points behind leaders Bruges.
(Reporting by Robert-Jan Bartunek; editing by Ken Ferris)
