The company will supply and transport 5.2 million tonnes of waste wood to the facility over the term of the deal, starting in 2017.
The contract is the third major biomass supply deal Stobart has won in four months.
Stobart is not taking part in the financing of the Rotherham project but the company said it expects it to achieve financial close in the next two weeks.
Stobart Energy & Infrastructure CEO Richard Butcher said: "This agreement means that in the last four months alone we have secured additional supply volumes for the Stobart Energy division totalling some 750,000 tonnes per annum from 2017 onwards through three long-term, index-linked contracts."
"We continue to strengthen our market leading position in the biomass supply market and are encouraged by the momentum in this business."
Earlier in 2015, Stobart secured a contract to supply 250,000 tonnes of waste wood per annum to a biomass facility that will be built at Margam, South Wales.
Stobart sources and delivers fuel to biomass plants under long term contracts. The company currently has agreements to deliver 1.75m million tonnes of fuel per year to the UK biomass market.
The company intends to deliver two million tonnes a year by 2017/2018.
