Councillors voted through the incinerator plan, which has run up against stiff local opposition, by seven votes to five on Thursday.
Kier is believed to have secured the civil engineering package for the controversial £140m plant, which will be run by German firm MVV under the 25-year, £800m PFI deal with local councils in the region.
The civils element of the scheme is understood to be worth up to £40m, and an estimated 400 jobs will be created during construction.
The incinerator is designed to handle 250,000 tonnes of rubbish a year, which would generate 57,000 tonnes of bottom ash.
MVV plans to build a plant at a quarry in nearby Buckfastleigh to turn the ash into roadbuilding material.
Dockyard operator Babcock Marine is contributing to the building costs in return for using waste heat and electricity to power the shipping complex, which spends around £15m a year meeting its energy needs.
MVV plans to commence construction next year with the plant scheduled to begin operations in 2014.