It picked up the business following a pitch against the incumbent, Droga5.
The agency will now be briefed to create a marketing campaign, including TV, press and poster and digital, to run across nine markets.
Publicis' New York office previously handled the global Malibu account but lost the lead creative duties on the business to Droga5 in 2007.
However, it worked on global implementation duties for Malibu's most recent TV campaign in June 2008. That push consisted of two ads that showed people in cities being influenced by the Caribbean mindset.
One execution showed people going about their daily business wearing flip-flops, while another saw a reporter playing Frisbee.
Cyril Claquin, a senior vice-president at Malibu, said: "Publicis London demonstrated genuinely innovative thinking, and delivered exciting creative work that has strong potential to give Malibu real social currency and breakthrough among a highly exposed consumer target."
At the same time, Pernod Ricard is moving its Malibu Kahlúa International brands division, which contains Malibu and Kahlúa, into the recently acquired Absolut Company in Stockholm.