The £185m plant, set to be operational by 2014, will create up to 300 jobs during construction.
Once operational it will be able to treat 350,000 tonnes of waste producing electricity for 50,000 homes in the city.
Howard Ellard, Viridor’s business development director, said: “We are pleased to be taking this important project to the construction phase.
“By 2014 Trident Park EfW will help local authorities and businesses to transform their residual waste into much-needed renewable energy.
He added: “The appointment of the CNIM and Lagan joint venture company is part of a long term working relationship with both organisations that we expect to strengthen over the next few years.
Viridor is already working with CNIM on construction of its energy-from-waste facility in Ardley, Oxfordshire.
Groundwork preparation is expected to commence within the next few weeks with the main construction due to begin in the summer.