The decision follows a recommendation by a planning inspector that the plant should be given approval following a public inquiry held in Trafford in November 2012 and the granting of an environmental permit to operate the plant in October 2012.
Trafford Council rejected the plans back in 2011.
The two-year construction phase could now start in 2014.
The £70m plant will generate electricity from 200,000 tonnes a year of biomass – mostly scrap wood, Peel says.
Peel Energy project manager Jon England said: “We would like to thank both the secretary of state and the planning inspector for giving the plans a fair hearing. We realise that applications like these are not easy. However, these are exactly the kind of decisions that are required if the UK is to meet its renewable energy targets, reduce reliance on imported energy and avoid valuable resources going into landfill.
“We are very pleased with the outcome and look forward to taking the project on to the next stage, ultimately delivering renewable energy and jobs for the region. We will continue to inform the community about forthcoming phases of the development.”