Anne-Marie Drozdz, from Hinckley, Leicestershire, was found in the property where she was staying in Ubud on Thursday.
A local man has been arrested amid reports that Bali police are linking the death to a robbery.
A spokeswoman for the Foreign Office would not confirm any details but said: "We are aware of the death of a British national in Bali and are providing consular assistance to the family."
Ms Drozdz, believed to be in her late 40s, had travelled around the world teaching at international schools and, according to her LinkedIn profile, last worked in Hanoi, Vietnam.
Her brother Gregory Drozdz said the Bristol University drama graduate had gone to Bali to set up a social enterprise to help improve young people's lives on the island.
Mr Drozdz, 55, said his family was consumed with "overwhelming grief".
He said: "We were contacted by the Foreign Office on Friday. They told us it appeared my sister had gone back to her villa in Bali and that there had been some kind of scuffle involving a burglary.
"My brother had only spoken to her by email a few weeks ago and she seemed very happy.
"I had sent her birthday greetings for her 49th birthday on April 29."
Speaking of the loss, Mr Drozdz said: "It's gut-wrenching. You never expect it's going to happen to you and your family. ."
He said his sister, who was born and grew up in Hinckley, had been a supply teacher in the town, but felt that her "true vocation was overseas".