The man, known locally as Steve, was found last week on a derelict plot on Priory Road, where the old Duncan Edwards pub used to stand.
Residents told the Express & Star he had been sleeping rough there in a tent for several weeks.
Dudley Council’s homeless team said they had been trying to help him by giving him food and offering a place to stay.
The authority is now investigating the cause of death.
Ian Austin, the Labour MP for Dudley North, said: "It is not yet clear exactly what happened to Steve, but it's a scandal that homeless people are dying on the streets in Britain today.
"Local people had contacted me about Steve and I had talked to Dudley's homelessness team to make sure he was getting help.
"I think they are working hard to help people, but it is not just a question of emergency accommodation because council and NHS cuts have hit the support and and help available for homeless people and benefit changes like housing benefit cuts and sanctions have made it all much worse.
"The number of people sleeping rough has soared – not just in major cities, but even in places like Dudley.
"The Government's policy is to halve it in five years and deal with it by 2027, which I think most people will think is hopeless when people like Steve are sleeping rough on the streets."
Councillor Laura Taylor, cabinet member for housing, said: “Tragically, we can confirm a man who had been sleeping in a tent on the Priory estate was found dead by two Police Community Support Officers (PCSOs) on Sunday January 21.
"Investigations are still ongoing to determine the cause of death.
“The man was known to us as a rough sleeper, and our officers had been out to visit him several times to offer assistance and shelter in a bid to help him.
“The council is part of a multi-agency group which includes social care and mental health professionals among others.
"It works with individuals we know are sleeping rough, with the sole aim of helping them off the streets. We are strongly committed to helping those who are genuinely homeless.”
Home Office figures show the number of people sleeping rough on Britain's streets has rocketed by 73 per cent in three years.
In the Black Country the number of rough sleepers has tripled since 2011.