Charlie and Gayle Anderson, 74 and 71, had retired to the Caribbean island after living in Manchester.
They had four grandchildren and one great-grandchild 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.
A police officer told Jamaican newspaper The Sunday Gleaner that their bodies had wounds to the face and neck.
Deputy Superintendent Throyville Haughton said Mr Anderson’s body was found not far from Mount Pleasant Primary School.
Mrs Anderson’s body was found at a different location.
The couple’s sons said they were devastated at the loss of their parents, who were just beginning the next chapter of their lives.
In a statement, they added Our parents Charlie and Gayle enjoyed a long and happy marriage.
They were hard-working 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.
News Source SkyNews