This is estimated to be completed by November 2027.
A total of 227 new homes will be delivered, all at affordable rents.
SWT have said the funding will ensure a “smooth transition between phases” and “quicken the pace” of the project.
Executive member for housing, Cllr Fran Smith, said: “The approval of these recommendations will assist the next phases of the project.
“It will provide certainty and security to the North Taunton Woolaway Project tenants.
“Not only is this a significant step toward zero carbon using renewable heat and power, but it forms an essential part of our commitment in offering a choice of good quality housing for our residents.