"They’re having a small intimate ceremony barefoot on the beach in Little Hall’s Pond Cay,” the Daily Star reports.
"Afterwards they'll have a barbecue where some of Johnny's musician pals are going to perform, followed by limbo dancing. Neither Johnny nor Amber want a big, glitzy Hollywood bash. They are both very private."
It has also been claimed that Johnny, 50, wants The Rolling Stones to play at his wedding.
A source told Now magazine: "The wedding plans are at an early stage. But the one thing Johnny does know is he wants Keith and the guys there. He might even ask to join them on a track or two."
The couple sparked rumours that they were engaged in January when Amber, 27, was spotted in LA with a sparkling ring on her engagement finger.
A representative for the pair confirmed the news just days later to US Weekly magazine.
"The proposal happened a while ago," a source told the magazine. "She just didn't wear the ring."
"Of course they couldn't be happier to be engaged and are excited to share the rest of their lives together," another source told People.
Amber and Johnny first met in 2011 when they starred together in The Rum Diary. It wasn't until the beginning of 2012 that they were linked romantically after the breakdown of Johnny’s 14-year relationship with Vanessa Paradis, with whom he has two children, Lily Rose,14, and Jack, 11.
Johnny reportedly called Vanessa to tell her that he had proposed to his Rum Diary co-star and the 41-year-old gave the couple her blessing.
"There's no drama," a source told US Weekly. "Vanessa wished him happiness. She's not bitter, she's happy."