Jan Bennett, 67, was attacked while walking her dogs near her home in the village of Malomir, around 200 miles east of the capital Sofia.
Mrs Bennett had only recently moved to the area with her disabled husband, having previously spent a number of years living in the Turkish coastal resort of Altinkum, where they were active members of a local church group.
Her 62-year-old husband is said to have been admitted to a local hospital where he was being treated for shock.
Police said a local man, Ivan Georgiev, 40, had been arrested on the basis of DNA evidence.
The Telegraph quoted a friend, restaurateur Karin Dalbak, saying: "You coped with life without complaint even when times were difficult. Truly a beautiful lady with a heart of gold. The world is a poorer place without you Jan."
A Foreign Office spokesman said: "We can confirm the death of a British national in Bulgaria. We are liaising with Bulgarian authorities and have met with the family to provide support at this difficult time."
Ms Bennett had been the secretary at St Mary's ecumenical church in Didum, Turkey, before moving to Bulgaria three months ago.
Fr Maurice Ryan from the church told Premier's News Hour she was a devout Christian.
He said: "She was very sensitive to people's needs and so on. What amazed me was that it was when her husband became ill she then re-joined the Church again, it was almost like a spiritual rebirth."
The vicar said her husband was very ill and her death had been "very difficult for him".
"He's now been taken to the local hospital where they're looking after him.
"Jan always thought that it was Nick who would die first, not herself."
Premier's Des Busteed speaking to Fr Maurice Ryan on the News Hour: