The body of Victoria Sloss was found on the banks of the River Clyde on Saturday morning by a member of the public.
The 23-year-old, who lived in Glasgow, had been dropped off by a silver-coloured taxi in Seaward Street, in the Kinning Park area of the city, at around 4.30am on Friday.
She was found at around 9am on Saturday in Napier Drive, Govan, opposite Scotland's Riverside Museum of Transport.
Police said her death was not thought to be suspicious.
It is believed Ms Sloss, who is originally from Oban but moved to Glasgow to study, may have drowned.
Detectives are desperately trying to piece together her movements after she got out of the taxi.
They are appealing for anyone with information to come forward.
Ms Sloss is described as being around 5ft 6in with a slim build and very long brown hair.
She was wearing a white T-shirt, maroon jumper, blue legging jeans and knee-high beige UGG boots.
Ms Sloss was reported missing when she failed to return home after the night out.
Friends posted messages to Ms Sloss, known as Vicki, on social networking sites.
Lesley Ann Paterson said: "Such a tragedy. Rest in peace Vicki and my thoughts and prayers are with all your family and friends."
Members of the Oban community also expressed shock at her death. Gavin Owens said: "Rest in peace Vicki Sloss. Such a shock to the whole of Oban."