White Stripes frontman Jack White, whose ex Renée Zellweger was married just last month, is now a married man himself, according to a posting on the band’s Web site.

White exchanged vows with model Karen Elson (who appears in the group’s “Blue Orchid” video) in the Brazilian city of Manaus on Wednesday, according to the statement, which the band’s rep confirmed to PEOPLE. Elson’s reps declined comment on the model’s nuptials.

According to the Web posting, the wedding took place “on the confluence of three rivers – the Rio Negro, the Solimones and the Amazon,” and was officiated “by a traditional shaman priest on a canoe at the exact point where the three rivers met.”

The ceremony – at which Stripes manager Ian Montone served as best man and Stripes drummer Meg White was maid of honor – was attended “by a small party of close friends” and “was immediately followed by a blessing by a priest at a Catholic cathedral called Igreja Matric,” the posting goes on to say.

The wedding seems to have caught everyone by surprise, including the band’s own rep. “I didn’t know,” Chloe Walsh tells PEOPLE. The White Stripes plan to perform in Europe during the summer before touring the U.S. in August, “so I don’t imagine there will be much time for honeymooning,” Walsh adds.

The Web statement also says: “This is the first marriage for both newlyweds,” though in 2003 the Detroit Free Press located a 1996 marriage document showing that Jack and Meg White were married. A divorce took place four years later.

Jack, 29, split from Zellweger after a year-and-a-half-long relationship last year. The Cinderella Man actress married country star Kenny Chesney on May 9.

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