The 54-year-old man’s body was discovered at the facility in Leodis Way, Stourton, in the early hours of Wednesday morning.
Officers from West Yorkshire Police were called to the scene at around 12.50am, although the death is not being treated as suspicious. The coroner’s office has been informed.
Mail centre manager at the Royal Mail Leeds site, James Jack, said: “Everyone at Royal Mail is deeply shocked and saddened by our colleague’s death.
“He was a much valued member of the team and he will be sorely missed by all his colleagues and friends in Leeds.
“Our deepest sympathy and thoughts are with his family and friends at this very sad time.”
Royal Mail’s Leeds plant is the second biggest in the country, serving seven postcode areas, including Bradford and Harrogate.