The US, China and the UK are its three top markets and other key territories are Italy, France, Germany, Hong Kong, Korea, Australia, Canada, Spain, Mexico and Brazil.
Havas Media said it will handle "the full range of media including social and programmatic".
Annual billings are undisclosed but the crystal jewellery business has expanded rapidly and doubled its geographical spread since Zenith, the incumbent agency, won the global account as part of a consolidation in 18 countries in 2008, when media spend was estimated at only €22m (£18.6m).
Privately-owned Swarovski has revenues of over €3bn a year.
Dominique Delport, global managing director of Havas Media Group, claimed the agency group has "a shared vision and passion" with Swarovski.
"We have a mutual focus on digital transformation," Delport said. "We know how important it is to keep the value that Swarovski has built up since 1895, but to also keep moving forward so that Swarovski can continue to design and deliver for the future."
Alessandro Vergano, senior vice-president of branding, communication and media at Swarovski, thanked Zenith for its "great work" over the last nine years. Havas Media takes over in January.
He said: "We are confident that we have found the right partner to deliver strategic support, operational set-up and digital transformation."
Note: An earlier version of this article reported that Havas won the account in "a competitive pitch against rivals, including the incumbent Zenith".
But Zenith said it did not take part in a pitch. A spokesman for Zenith said: "We are surprised by Swarovski’s decision to move the account without a competitive pitch, especially given the exceptional quality of work that we have consistently delivered over the past nine years.
"We will continue to work with Swarovski until they transition the business at the end of this year."