Stephen McGowan, 23, was found with serious injuries in a common close in the Inverclyde town's Tobago Street at 03:20 on Sunday. He died at the scene.
Police also cordoned off an area of Lynedoch Street, which they said was linked to the same incident.
The murder inquiry was launched following a post-mortem examination. Police have appealed for information about Mr McGowan's last movements.
Det Ch Insp Jim Smith, from Police Scotland's Major Investigation Teams, said: "I am still keen to speak to anyone who may have seen or spoken to Mr McGowan in the vicinity of the James Watt Wetherspoons Bar, Waterline Bar or Reds Nightclub in Cathcart Street, Greenock, around 0320 hrs on Sunday 27 July 2014.
"In particular I am anxious to trace and speak to a man who was seen waiting for a taxi in Cathcart Street at this time.
"He was wearing dark trousers and training shoes and had his top off.
"This man may be able to provide vital information that could assist our enquiries and we urge him or anyone who recognises him to contact police immediately on 101, or alternatively through Crimestoppers on 0800 555 111, where anonymity can be maintained."
Police have launched a murder inquiry after the death of a man in Greenock.