It will be the only one of its kind in the UK and one of only a handful of its type in the world.
The Glasgow Recycling And Renewable Energy Centre, which should be finished early in 2016, will help the city meet tough new Scottish Government recycling rates.
Councillors approved the plan despite dozens of objections from locals.
It will be sited on the existing council waste facility at Polmadie and it is claimed the scheme will save the council £254m over 25 years in reduced landfill charges.
The plant, which will be run by Viridor on a 25-year lease, will operate 24 hours a day, seven days a week. It will create 254 jobs.
Council leader Gordon Matheson said: "This is great step forward for Glasgow on the road to becoming one of Europe's most sustainable cities.
"Without this facility, we would be faced with the depressing prospect of piling millions of tonnes of waste into the ground over the coming years and we would also pay through the nose to do it.
"Our competitors – the likes of Sweden, Denmark and Holland – have the highest recycling rates in Europe. They achieved this by embracing a mix of modern but proven technologies that boost recycling and recover energy from what remains.
"This is an approach that has huge potential in Glasgow by putting the city's waste to work for the benefit of its people."
Domestic green bin waste from across the city will be taken to the new plant and materials that can be recycled will be removed. Organic materials, such as food and garden cuttings, will go into a plant that turns them into natural gas, which will be used to power the plant.
The residue will be used to produce a gas that will be burned to generate electricity that will power neighbouring homes and properties.
Steven Don, Viridor's Scottish regional manager, said: ""This facility will transform the way in which the city's annual 200,000 tonnes of domestic green bin residual waste is managed."