A surveyor working at the viaduct site off Whitehall Road in Holbeck made the discovery at around 11.30am.
Security guard describes finding man's body beneath derelict railway archesHe was lying in an archway underneath the disused structure behind the Number One Leeds office building.
Man found dead under Leeds railway viaductHe is not believed to have been homeless.
West Yorkshire Police said:-
"The death of a man found on Whitehall Road is not being treated as suspicious, a file will now be prepared for the coroner."
A security guard who was one of the first on the scene described seeing bloodstains on the ground and the brickwork.
Mohammed Maroof accompanied the surveyor to check on the man's welfare and they found him to be unresponsive. They called an ambulance.
"He called me over as I have a key to the site and we both had a look around. He was lying at the back of an arch and we both shouted to him, but he didn't respond. We were scared to get too close - we could see his skin was really pale. We called an ambulance and waited for the paramedics, who said straight away that he was dead.
"He hadn't moved at all in about half an hour. The police came and sealed it off.
"He didn't look like a homeless person or someone who'd been sleeping rough. There was lots of blood around the arch and on the bricks. He didn't have a blanket or any covering but there was a jacket that had been left on the edge of the archway. It was hard to tell his age.
"I'm really shocked - I've been in security for 19 years and never seen anything like this. The police said they'd keep me updated."
The viaduct - which used to carry a railway line from Farnley into a now-demolished station just off Wellington Street - is currently the subject of a development scheme which could see the arches become shops, cafes and bars. Surveying work began several months ago.
The arches were also used for the filming of a BBC adaptation of Agatha Christie's Poirot novel The ABC Murders in July. Extras in 1930s police uniforms were seen close to the spot where the body was found. The drama is due to be screened this Christmas.