Wallace said this funding would help support with the costs of the start-up phase of the project as the trust worked to finalise its business plan and secured further funding.
The council's original recommendation was to provide a one-off grant of $20,000.
However, councillor John Robson put forward a motion to double the grant amount to $40,000 and urged his fellow councillors to support the motion.
"I think we need to look at the what the Tauranga men's shelter was given for its set up costs, and given the very tight timeframe to set up the Awhina House... I think we can justify $40,000," he said.
Cr Kelvin Clout said given this would be seed funding, and other funding providers would also be involved, he agreed with the recommendation.
Wallace told the Bay of Plenty Times that she and other trust members were "thrilled" the councillors had all supported this initiative, especially in light to the recent begging and rough sleeping bylaw.
"It shows us that the hearts of the councillors are in the right place and they do really care about these vulnerable people in our community," she said.
Wallace said she was not in a position at this stage to reveal who owned the building nor how much the annual lease costs were.
"We will take over the lease in early January and hope to open the shelter sometime in February," she said.
Wallace said to get the shelter operating, between $80,000 to $100,000 would be needed and the trust would also need to seek further funding to cover ongoing operational costs.
Funding applications to help with start-up costs were being lodged with the Tauranga Energy Community Trust and the Acorn Foundation, she said.
The Bay Trust had also provided "some toolbox funding" to assist in developing a strategic plan for the shelter.
Close to $20,000 in private donations had also been received, she said, including donations from four city councillors and a $10,000 donation from local man Bonnie Ohlson from Watchmen Security.
The trust welcomed any support both in cash and/or support services, she said.
More details about the project can be found on the Community Angels Facebook page.