Police said her body was found at sea about 62 miles from where she went missing.
Some members of the family flew out to help search for her, including her mum Linda, dad Phil and brother Harry.
Amelia's brother, Harry Bambridge has confirmed the news on social media, he wrote: "I've just seen her and I can confirm it's my little sister Amelia. I'm so sorry to all her friend and family, there's nothing more I wanted then to bring her back alive..."
Miss Bambridge, from West Sussex grew up attending St Michael's Catholic church in Worthing, where the Bambridge family held a prayer vigil for her on Wednesday evening.
Father Christopher Ingle from St Michael's told Premier: "We are absolutely devastated. Everyone is very upset as you can imagine.
Fr Christopher said: "I've known her since she was a baby, she was baptised here as a baby, she had her first communion here."
Remembering Amelia Bambridge, the priest explained: "She was absolutely fabulous, a very courageous, very strong and wonderful person.
"Prayer is really powerful, to give us strength, courage and comfort. Please pray and ask the Lord to comfort Amelia's family at this time and to keep her in your hearts to remember," he added.
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