In a note on her Web site posted Sunday, Anderson described the nuptials as: "The best most romantic wedding of all time."
"She was the most beautiful bride I've ever seen – like a modern-day Brigitte Bardot," Jimmy Choo owner Tamara Mellon tells PEOPLE about Anderson, who wore a white string bikini to her nuptials. "Kid Rock was a total rock star. He gave her a good kiss. Everybody was crying." Adds Elton John's husband David Furnish: "It was a real rock n' roll wedding."
Anderson says she plans to post photos of the event "from inside the boat that we took" on her Web site soon.
The marriage, however, is not a legal union, according to the mayor's office in Saint-Tropez. "It was just a celebration," said a spokeswoman for the office, who explained that in France couples are required to have a civil wedding at the mayor's office in order for it to be legal.
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Anderson and Rock, 35, began dating in spring 2001. They became engaged on April 11, 2002, in the Las Vegas desert, but split the following year. Still, when they ran into each other early this month in Saint-Tropez on a mutual friend's yacht, the feelings were still there.
"It was like we'd never been apart," Rock told PEOPLE on July 11. "(I) love her to death." Anderson announced their engagement on her Web site on July 18.
The British Columbia-born Anderson has two sons, Brandon, 10, and Dylan, 8, with ex-husband Tommy Lee, to whom she was married from 1995 until 1998. Her kids were with her when she ran into Rock earlier this month. "It was so nice to see them," Rock told PEOPLE.
Detroit-born Rock has a 16-year-old son, Robert James Ritchie Jr., whose mother is Kelly South Russell, a Detroit auto worker.