The £120 million scheme, designed by commercial giant RTKL, is being backed by American casino operator Las Vegas Sands, which owns the famous Venetian Resort Hotel.
The development, which will sit on the club's Albion car park site next to Ibrox Stadium, is the first proposed regional casino to been given the go-ahead since the government's Gambling Bill was passed in April this year.
Part of a wider masterplan aimed at regenerating the city's rundown Hinshelwood area, the complex will also house restaurants, cafés and bars as well as the new Ibrox Community Centre and a roof-top football pitch.
Rangers chairman David Murray said: 'We are delighted that the city council has approved our vision for a world-class entertainment complex.
'The decision puts Glasgow significantly ahead of the rest of the UK in the race to secure the regeneration that a regional casino licence will bring.'
He added: 'This development will bring so much to the community around Ibrox, not just in terms of better housing and leisure facilities but also through employment opportunities.
'The creation of our vision will put Glasgow and Ibrox firmly on the map as a top-class leisure and tourism destination.'