A Sussex Police spokeswoman said it was possible the corpse had been lying unnoticed for days beneath the busy walkway.
Officers believe the man was beaten, possibly with a weapon, and as a result suffered a severe wound to head.
Three volunteers who were checking up on the wellbeing of rough sleepers made the grim discovery at around 8:30pm.
They saw a figure lying under arches next to the golf course beneath a duvet with the head covered. But to their horror, when the volunteers pulled back the cover they discovered a badly beaten body.
The victim, who was originally from Hastings and in his 40s, had been living on the streets in Brighton and Hove for years - and police said he may have known his killer.
Yesterday (February 12) officers fanned out across the city to speak to rough sleepers about the brutal attack while divers scoured nearby Hove Lagoon for a murder weapon.
Bec Davison, deputy director of the Brighton and Hove-based charity CRI, said the victim was well known to services in the city.
She said: “We have worked with him for a long time – we had a good relationship and he seemed quite happy.
“It's extremely distressing for everyone here. The saddest thing is that it's quite easy for someone who's a long time rough sleeper to become invisible.
“But this man was vulnerable and he had a real story.”
The charity workers who found the body were volunteering for Project Antifreeze, a Brighton and Hove-based homeless project.
Julian Haddow, the project's leader, said the three volunteers had been traumatised by their discovery but that they would be given “full support”.
Detective Chief Inspector Ian Pollard, who is the leading the investigation, said “no stone would be left unturned” in the hunt for the man's killer.
He said: “"This was a vicious attack, the motive of which is not yet known nor how the deceased's injuries were inflicted.
“"I know the street community are very close knit - but I would appeal to them to please get in touch if they have any information that could help us with our enquiries no matter how relevant they think it is.
“This man was found next to a busy thoroughfare with cyclists, joggers and traffic. If anyone knows anything about what happened - please get in touch.”
Anyone who witnessed the attack or has any information that could assist police with their enquiries are asked to call 101 quoting Op Depot or alternatively leave an anonymous message with the independent charity Crimestoppers on 0800 555 111.
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