The Live Aid founder, 63, wed the actress in Rayol Canadel Sur Mer in the South of France, reported People magazine.
The couple have been together for two decades.
Geldof's eldest daughter, Fifi, hinted at the union on her private Instagram account in recent days, including last week when she posted a pic of herself in a formal dress "for an event later".
The happy news comes after a period of deep grief for the Bob, who lost daughter Peaches Geldof at age 25 to a heroin overdose last April.