Part of the Queen's Dock redevelopment, the arena will become a 'key addition' to the Scottish Exhibition and Conference Centre (SECC) - a cultural hub which sits on the banks of the Clyde.
The venue has been designed to be able to host a wide range of indoor events, from pop concerts to grand theatrical performances, and will overlook a listed boatyard crane.
The shallow-domed roof of the auditorium will be supported by diagonally latticed steelwork and will have a 'distinctive sloping appearance'.
Describing the scheme, a Foster's spokesman said: 'The main entrance is carved into a generous top-lit ground-level foyer.
'The second main foyer, at high level, has its own distinct character with views south through a glazed facade, over the public square to the river.'
And Chris Connell, the partner in charge of the project, added: '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 new public spaces.
'By reinventing the approach to the SECC, the building will be central to the Queen's Dock redevelopment.'