Depp, 51, and Heard, 28, are all set to walk down the aisle next weekend, reported People magazine.
The actor has owned the 45-acre island - with beaches named after his children, Lily-Rose, 15, and Jack, 12, and his idols Hunter S Thompson and Marlon Brando - for more than a decade.
Representatives for both of them have not responded to requests for comment.
The couple met on the set of 2011's 'The Rum Diary', but didn't start dating until 2012, after Depp split with longtime partner Vanessa Paradis.
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