TRC's housing general manager Neil Porteous said it was a pleasing outcome.
"We are pleased to have come to an agreement with Ms Rauti. She has now moved into a new Tamaki Housing property nearby."
Rauti told the Herald she was unable to comment today.
TRC's earlier offers of a new home had been rejected by Rauti, who wanted to stay in the house that she'd been given the lease for in 1999 and where her mother had lived since the 1980s.
She had said alternative homes were not suitable for her needs as they were too damp, or the two-storeyed homes were too difficult for her to access.
Rauti's house was one of 2500 state houses pinpointed for demolition to make way for 7500 new homes within 10 to 15 years.
The regeneration programme would see a net addition of 5000 "affordable" and market-priced homes, while the number of social houses would stand at 2800.
Rauti and her supporters opposed the plans, which they saw as a mass sell-off of state housing.