The TV star was held by police over the weekend and called before a judge in Bridgetown on Monday, according to The Sun.
He was fined £250 and released immediately. Edwards was told that any repeat offence would see him end up in jail.
A police spokesman commented: "Edwards was arrested after acting suspiciously on the street and was found with an amount of cocaine, but officers believed it was for personal use.
"He has been allowed to continue his holiday."
The Cooking The Books presenter is still expected to celebrate his engagement to Lydia Metz later this week.
A source said: "She won’t be too annoyed as she is very laid back, so there is no risk of her dumping him. She is used to his partying. It’s his mum he needs to worry about.
"She’s not going to be impressed."