The scheme being promoted by a joint venture between the county council and York city council still needs to obtain planning permission.
When consent is obtained, construction will take place in several phases over the course of next year and create around 400 building jobs before the huge waste processing site is due to become fully operational by 2015.
The two authorities estimate the quarry site waste scheme, located between York and Knaresborough, would allow them to cut their waste management bills by £320m.
But there is fierce local opposition to the plan and protestors stage a demonstration outside the county hall in Northallerton as the council voted 49-19 in favour of awarding the job to AmeyCespa.
Allerton waste recovery park will also include a facility that mechanically sorts and reclaims 20,000 tonnes of recyclable materials left in the residual waste each year and an anaerobic digestion plant for garden and food waste that will also generate electricity.