He has been identified as Terrell Davis, 27, who lived in Lambeth. His next of kin are aware.
Mr Davis was found stabbed by members of the London Ambulance Service in Ramillies Close, SW2 at 6pm.
Officers attended, along with colleagues from the London Air Ambulance, but Mr Davis was pronounced dead at the scene.
A 21-year-old man was arrested in south London yesterday, 24 November on suspicion of murder and remains in custody at a south London police station.
Detective Inspector Chris Wood, Specialist Crime (Homicide) is investigating. He said: “An arrest has been made and we continue to follow a number of leads following this tragic loss of a young life. Terrell’s family are distraught and we are providing them with support via specially trained officers as they begin to grieve for him.
“We have spoken to a number of people in the local community about this terrible incident, but I believe there are others who have yet to come forward and tell us what they know.
“The answer to what happened to Terrell lies somewhere in the community and there will be people with key information that could help us bring justice to Terrell’s family.
“Police and communities must work together to combat violent crime. If you are concerned about telling us what you know, or would not usually interact with the police, I can assure you that anything you tell us would be in the strictest of confidence.”
BCU Commander for Southwark and Lambeth, Colin Wingrove, said: “This is a horrific incident and our thoughts are with the victim’s family, who have lost a loved one in such tragic circumstances.
“Our Specialist Crime colleagues are investigating this terrible incident and locally we are providing every support.
“I want to reassure local residents that there will be an increased policing presence in the area over the coming days.
“We must work together to remove violent offenders and knives from the streets and in doing so make our communities safer”
“I would urge anyone who has information they would like to share to approach the officers in the area or call 101.”
Information can also be passed anonymously via Crimestoppers 0800 555 111. Any witnesses or those with information are asked to call 101 quoting CAD 5428/22Nov.