"It will be Australia's biggest and best contemporary art gallery," the premier told reporters on Sunday.
"This is a special project."
NGV Contemporary is the centrepiece of an arts precinct redevelopment that will create about 10,000 jobs during construction.
New bars and cafes will be established along the Southbank arts precinct, which already includes the NGV and the Arts Centre Melbourne.
The revamp will open up some 18,000 square metres of new and renewed public space and provide an easy pathway from St Kilda Road to the Yarra River.
Mr Andrews said Victoria's creative industries are responsible for about a quarter of a million jobs so they need to be supported.
"Those livelihoods are pegged against visitors coming here and enjoying what is an outstanding offer but one that has to be better," Mr Andrews said.
The project has been kickstarted with $208 million from the state government and Mr Andrews is hoping arts-loving philanthropists will help to fund it.
"I think that very substantial amounts of money will be able to be sourced from very generous Victorians," the premier said.
Under the project, the Arts Centre will also be upgraded while 1 City Road will become a creative hub, home to the Australian Performing Arts Gallery and an expanded Australian Music Vault.
"We have many fantastic facilities here but some of them are showing their age," Mr Andrews said.
"We won't retain our title as the nation's cultural capital, and one of the great cultural cities of the world, if we rest on our laurels."
NGV Contemporary will be about three times the size of the the Museum of Old and New Art in Hobart, the premier said.
Architects will soon be appointed and the government is hoping construction will begin within 18 months and be completed by the mid-2020s.