Kay claims she fell overboard on the cruise ship Norwegian Star.
The woman gave an interview to the Croatia news service HRT after her ordeal, in which she said: "I was in the water for 10 hours, so these wonderful guys rescued me".
Her disappearance sparked a panicked search and the ship returned to the spot where they believed she had fallen and carried out at least four passes before abandoning the search.
Mr Walker, based in Miami, Florida, said he believed that the Norwegian Star, which is owned by the Norwegian Cruise Line (NCL), had abandoned the search and was continuing its course to Venice when the woman was rescued.
"In the morning of August 19th, a guest went overboard as Norwegian Star made her way to Venice", the company said. "We are very happy that the individual, who is a United Kingdom resident, is now safe and will soon be reunited with friends and family". "The Coast Guard was notified and a search and rescue operation ensued", a spokesperson for Norwegian said in a statement.
The woman speaks to Croatian media after her ordeal
The Sun named her as Kay Longstaff, a 46-year-old corporate flight attendant on private jets. However, she still managed to explain that she was in the water for 10 hours. She was taken to shore to be treated at hospital and will soon be reunited with her family and friends.
The circumstances of the incident were being investigated and the British Embassy in Croatia was informed.
"We are pleased to advise that the guest was found alive, is now in stable condition", the cruise company said in an email to The Washington Post.
The moment of rescue. the woman is brought aboard the Coastguard boat.
A British woman was saved in the Adriatic Sea after falling of a cruising ship.More news: Pierre-Emerick Aubameyang has shocker as Arsenal lose at Chelsea