Deckhand Bethany Smith, 18, of Denbighshire, was working up a mast of 196 ft (60m) luxury schooner Germania Nova, berthed in Port Antonio.
Yacht management company Hill Robinson, which charters the Germania Nova, has started an "immediate investigation".
Hill Robinson partner Niall Robinson said they were "doing everything to support the family and friends".
Ms Smith left her home in Glyn-Dyfrdwy to sail around the world with her family 10 years ago in their yacht "Cape" along with her younger brother Bryn.
After spending three years cruising around the Mediterranean, the family sailed on to the Canary Islands and west Africa where they spent a further two years before crossing the Atlantic in March 2012.
They have since toured the Caribbean islands extensively, writing about their travels online.
Writing in a blog last year, Ms Smith's mother said the family were delighted she had got a job as a trainee on the Germania Nova.
A crowdfunding page set-up to help her family said the yacht was berthed in Port Antonio when she fell and Ms Smith died in hospital from multiple injuries.
Jamaican police said Ms Smith was cleaning the Germania Nova's mast on Tuesday afternoon when the ropes became undone and she fell on to the deck.
"We are desperately sad to confirm that a tragic accident has occurred on Germania Nova leading to the fatality of a crew member," said Mr Robinson.
"The crew member's next of kin have been informed and our thoughts are with the family, friends and fellow crew members at this very difficult time."
A family friend who started a gofundme campaign to help the family meet the costs of the tragedy said Ms Smith would be remembered for being "a generous person and a ray of sunshine who brought laughter and music into the lives of those she met".
The memorial fund has passed its target and raised around Â£10,000 (US $12,185) to help her family pay for the travel and funeral costs.
Family friend and Llangollen councillor Stuart Davies described the shock felt in the local community, where Ms Smith's grandmother still lives.
"It's tragic. As a parent of two daughters I cannot imagine how they are feeling," he said.
"They were about eight or nine when they went. It was their life - it revolved around yachts, boating and that."
An inquiry has been launched into how a teenager fell to her death on a luxury yacht in Jamaica.