The council heard the trust had $121,481 in available funds from income on the invested principle.
The Stewart Trust is set aside to be used for the relief of poverty. It has previously helped to fund the Tauranga Community Foodbank and Tauranga Moana Men's Night Shelter.
Awhina House is being established by advocacy group He Kaupapa Kotahitanga, who formed in August.
Chairwoman Angela Wallace said the decision was "great news".
The trust has leased a 13-bedroom property in The Avenues, which is being turned into an emergency shelter for Tauranga's homeless and displaced women.
In January the house was hit by thieves who took the washing machine, lawnmower, power tools and garden equipment.
In the wake of the theft, the trust was overwhelmed by donations.
The trust also secured funding from the Tauranga Energy Consumer Trust (TECT) ($65,000), the Acorn Foundation and Craigs Investment Partners ($15,000), Synergy Technologies ($20,000), Watchmen Security ($10,000) and BayTrust ($6000).
They hope to open early this year.