The body of Polish national Waldek Mural was found in Burley Park by a member of the public at about 7am on Saturday.
He had suffered multiple injuries to his body.
Two men, aged 30 and 32, were arrested on Sunday morning on suspicion of murder but have now been released without charge.
However, a third man, aged 41 and from Leeds, has been arrested and is in custody.
Mr Mural, aged 57, is understood to have lived in Leeds for at least the last five years and was known to frequent the Armley and Burley areas.
West Yorkshire Police have again appealed for information following his death.
Detective Chief Inspector Jim Dunkerley, of the homicide and major enquiry team, said: “We continue to appeal to anyone who believes they saw Mr Mural in the 12-hour period before his body was found in Burley Park to come forward.
“We know he was in the Town Street area of Armley the evening before and would urge anyone who was in that area to cast their minds back on whether they saw Mr Mural. We are also keen to hear from anyone who believes they saw him or who noticed any suspicious behaviour in the vicinity of Burley Park.”
Anyone with information should call HMET via 101 or Crimestoppers, anonymously, on 0800 555111.