The 12,500-seat venue would be built on the site of a car park next to the Scottish Exhibition and Conference Centre (SECC) and is the first stage of the masterplan for redeveloping Queen's Dock.
Designed by Foster and Partners, the £62 million arena would be capable of staging children's events, concerts, ice shows and sporting events.
The car park would be replaced by multi-storey car parks during the first stage of construction work in 2006.
"This is an arena like no other in the UK," said SECC group chief executive Mike Closier. "We have not been constrained by sporting events such as ice hockey to make it economically viable because our base of transferable business has afforded us the luxury of creating an arena that focuses on the entertainment experience."
It is estimated that the development could inject £50 million a year into the local economy and create 1,500 jobs, adding to the £114 million and 3,500 jobs currently generated by the SECC. "Scotland needs this venue. The SECC cannot accommodate any more arena-style concerts than it does at the moment," added Closier.
The arena could open in 2009. Its 40m-high front elevation would be clad in a translucent material that could be lit at night and carry projections to change its appearance to suit individual events.
Glasgow City Council leader Steven Purcell described it as "a hugely important project that will boost Glasgow's economy and give further momentum to the continued regeneration of the Clyde".
Chris Connell of Foster and Partners said: "This is an exciting opportunity to create a world-class performance venue for Scotland that will strengthen connections to the River Clyde and promote a series of public spaces."