"We're totally overwhelmed really. It's wonderful for the Sarjeant and the museum and certainly for the city, the region and the country."
As well as the $10 million for the gallery Government lobbed in another $400,000 for the upgrade of the Whanganui Regional Museum.
Ms Williams said achieving raising a matching $10 million in private donors had been "a long, hard road" and hadn't been easy.
"It's been very difficult and has had its highs and lows. There's been some conflict and lot of hurdles to jump but this news has made it all worthwhile," she said.
She said with the Government on board the trust's next mission was to get to the project to the finish line "and we'll do it".
The project, estimated to cost $34.9 million, will earthquake-strengthen the historic Queens Park building. The district council has contributed $5 million and about $11 million has been donated in cash and pledges from the community, private trusts and individuals.
The Government's money is subject to the trust raising the final $9 million by December next year and Ms Williams said that funding is expected to come in part from Lottery grant applications, corporate funding and more donations.
The district council has agreed to underwrite any cost overruns or shortfall in funding but she said she was confident the fundraising targets will be achieved.
The extension will double the size of the gallery and will honour the memory of Sir Archie Taiaroa. It will include storage and education facilities, large exhibition spaces along with room for retailing and events.
Design drawings have been done by Warren and Mahoney Architects and resource consents are already in place.
The Sarjeant collection was valued at $28.2 million in 2012 and, before moving to the temporary site on Taupo Quay, most of the collection was stashed away in the basement of the Queens Park building.
