The British grandparents, Charlie and Gayle Anderson, were married for 55 years and have been described by family as "hugely popular and loved by many".
The statement added: "They were just beginning the next chapter of their lives, retiring to Jamaica before this awful tragedy".
Their released by the Foreign Office said: "Our parents Charlie and Gayle enjoyed a long and happy marriage of 55 years and leave behind their four grandchildren and one great-grandchild".
They said: "They were hard-working people, building a business with integrity and making sure we were always provided for".
Former neighbour Kishore Singh, who lives on High Bank in Manchester, said the couple "were two of the most handsome people in the world, Charlie was like a father to me".
Anderson, 74, and his 71-year-old wife, were discovered on Friday at their home in Mount Pleasant, according to local media reports.
Jamaican police confirmed they were involved in another ongoing investigation but said they had not yet established a motive for the killing.
The statement added: "They were just beginning the next chapter of their lives, retiring to Jamaica before this awful tragedy".
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"We are completely devastated and ask for privacy at this extremely hard time".
Their former neighbours said the couple had "saved all their lives" to afford a large house on the island, which Mr Anderson had built himself.
Local newspaper the Sunday Gleaner quoted a police officer saying their bodies had been burned, and both had wounds to the face and neck.
He went on: "He would tell me 'I'm going home, I've worked in this country and now I want to go home and retire and enjoy my last few years".
According to the Sun, Mrs Anderson had reported fraudulent purchases on her credit cards totalling more than A$89,000 to police. We'd stand outside talking for hours.
While Jerome Heslop, a farmer from the community in Jamaica said: 'I am baffled by these murders.
Their family have said they are "completely devastated". Each time they are in Jamaica, they bring back shoes, clothes, tablets, food stuff, school items, and other stuff for residents.
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