Charlie and Gayle Anderson, who had four grandchildren and one great-grandchild, had retired to the Caribbean island after living in Manchester.
They were 74 and 71, and had been married for 55 years.
According to local media, their bodies had both been burned when they were found in Mount Pleasant on Friday.
Jamaican Newspaper The Gleaner, quoting a local police officer, also said both bodies had wounds to the neck and face.
The couple’s sons said they were “devastated” at the loss of their parents, who were “just beginning the next chapter of their lives”.
“Our parents Charlie and Gayle enjoyed a long and happy marriage,” they added in a statement.
“They were hardworking people, building a business with integrity and making sure we were always provided for.
“Charlie and Gayle were pillars of the community in Manchester and Jamaica, and were hugely popular and loved by many.
“We would like to thank our friends, family and community for their prayers and support.”