Police were called to a property in Woodside, Methley, following concerns for the man and woman.
The 69-year-old man and 58-year-old woman were found dead at the scene.
West Yorkshire Police said they were called to the property just after 10am on Sunday, April 28.
Their deaths are not being treated as suspicious.
A police spokesman said: "At 10.11am on Sunday, April 28, police were called to an address in Methley, Leeds, where a man and woman had been found dead.
"The deaths are not being treated as suspicious and the Coroner's Office has been informed."
An inquest into the man and woman's death has since been opened and adjourned.