The project is being developed at Allerton Park, near Knaresborough by North Yorkshire County Council and City of York Council along with AmeyCespa, Aberdeen UK Infrastructure Partners and Equitix.
Of the total financing, around £150m will be provided by EIB, while the remainder £33m will be funded by GIB.
The project will feature a mechanical pre-treatment facility to recover metal, paper and plastics for recycling, an anaerobic digestion facility to treat organic waste and produce about 6GWh of renewable energy a year.
The construction of the facility is anticipated to start in December 2014 with operations planned for 2018.
The facility will generate 203GWh of energy annually which will be enough to power more than 40,000 households in the region.
EIB vice president Jonathan Taylor said: "The European Investment Bank is committed to supporting investment in waste processing that reduces carbon emissions, uses waste to generate green electricity and lowers long-term costs for households."
UK Green Investment Bank chief executive Shaun Kingsbury said: "This innovative project is a best-in-class example of how local authorities can improve recycling and generate significant amounts of renewable power from household waste."
