Nicolai Brown was treated by paramedics after police were called to Moorfield Avenue, Armley, at about 9.20pm on Monday but died at the scene.
Officers had initially been called after reports that the 27-year-old was in a distressed state.
A 43-year-old man has been arrested on suspicion of murder and remains in custody.
According to Mr Brown’s Facebook profile, he was a former pupil of Allerton High School in Alwoodley and a keen gym-goer.
Several people have paid tribute to him on the social networking site.
Lisa Clark wrote: “Rip nicolai brown guna miss ya my mate love ya always.”
Dawn Woodhead added: “R.I.P Nicolai you was a great lad and treated my daughter’s with respect. You will be sadly missed by all mate.”
Police found Mr Brown fatally injured after searching the Armley area. They cordoned off a number of areas in the vicinity while investigations were carried out.
A post mortem was carried out on Monday afternoon to determine the cause of his injuries, but the results have not yet been released.
Detective Superintendent Nick Wallen, of West Yorkshire Police Homicide and Major Enquiry Team, said: “We are speaking with the dead man’s family who are understandably distraught about his death.
“We are treating his death as murder and a number of scenes in the vicinity are being forensically examined. We are trying to build up a picture of the circumstances surrounding the victim’s death and of his movements earlier in the evening in the time leading up to him being found in Back Moorfield Terrace.
“We would like to hear from anyone who witnessed anything suspicious in the area or who has any information that could assist the investigation.”
Anyone with any information is asked to contact the Homicide and Major Enquiry Team via 101 or call Crimestoppers anonymously on 0800 555 111.