John Morrison, 50, who lived in Milngavie, was found on Argyle Street at the junction of Dunlop Street at around 12.30 am on Saturday. He was taken to Glasgow Royal Infirmary where he later died.
Mr Morrison, a Liberal Democrat, was the leader of East Dunbartonshire Council from 2003-7.
Police said he had been assaulted, but an initial post-mortem examination proved inconclusive and the cause of death has not been established.
The area was cordoned off from early on Saturday and police officers are collecting footage from CCTV cameras in the area, near Argyle Street railway station and the St Enoch shopping centre.
Mr Morrison, a legal manager with Glasgow City Council since 1990, studied at Glasgow University from 1980-85.
He was first elected as a councillor in East Dunbartonshire in 1999, and became depute leader from 1999-2003.
East Dunbartonshire Lib Dem MP Jo Swinson said: "This is shocking news and my heart goes out to John's partner, family and friends.
"John was a skilful debater and effective leader of East Dunbartonshire Council. He dedicated decades of his life to public service, both in elected politics and at Glasgow City Council. This is a tragic loss."
Deputy Chief Whip Alistair Carmichael MP added: " For me he was not just a political colleague but a close friend whom I had first met when we were both students at Glasgow University.
"My sadness today is lifted only by many happy memories I shall always have of the fun times we shared.
"My thoughts are with his partner David, his daughter Kirsty and the rest of his family."
Former LibDem leader Charles Kennedy said: "This shockingly sad news sees the sudden passing of a great character and a memorable personality within the party.
"I first became friends with John at Glasgow University and was pleased when he succeeded me there as chairman of the Social Democrats in university union debating.
"He went on to make his mark both in the law and local government. It was a great pity that he was never able to deploy his talents at Holyrood.
"Our thoughts go out to his family at this time of such acute distress."