Veolia beat off competition from a consortium led by Covanta with plans to build the incinerator at Cross Green.
The plan will save the council almost £200m over 25 years by avoiding landfill taxes and generate enough electricity for 20,000 houses.
The design represents a new departure for waste plants, featuring a greenhouse-style main building made of glass and wood, covered with a living green wall of plants.
The building would include a chimney about 65m high, though its final height would be determined by the Environment Agency.
The plant will provide a combined heat and power off-take for use in the Aire Valley.
Waste ash is planned to go to an ash recycling plant in Sheffield where it will be processed for use as an aggregate.
Ultimately, 3.5% of the energy from waste plant input will go to landfill.
The government will now consider whether to approve the city council’s recommendation for preferred bidder.
Veolia will then carry out a full public consultation and submit detailed planning applications.
If the plant gets the final go-ahead, it is expected to be running by spring 2016.