Twyford said a process was being worked through to determine the exact amount of funding and number of places that Napier and Hastings would receive.
"Government will take a staged approach to expanding the programme into Napier and Hastings, which we expect to roll out next year.
Local housing advocate Anna Lorck said the move would "make a real difference" to the region's most vulnerable children and families.
"This model is proven to work as it makes housing people the first step, and then wraps the other social support services around them and integration within the community.
"In Hastings I've met and talked with children and families living in caravans, garages, and in hotels and living out of cars."
Napier Mayor Bill Dalton said the move would bay "a huge help" to solving a big issue in the city.
"People, I'm sure, sitting in their comfortable homes, do not realize how serious the homeless and over-crowding of properties is in Napier.
"There is a huge need for affordable housing - both for purchase and for rent - and I absolutely welcome anything that is done to help that position."
The mayor pointed out that the city council was also reviewing it housing and low-cost housing policy on an ongoing basis.
"It's something that we take very seriously."
Hastings Mayor Sandra Hazlehurst also welcomed the announcement.
"Housing First is a programme to house and support chronically homeless people, often facing multiple and complex issues.
"This is a good start to address the major shortage of housing in Hastings. I met with Minister Twyford last month with a team from council to talk about our urgent housing need, and it is positive and reassuring the Government has recognised that.
"This is something I am really passionate about. I have people in our community pleading for me to try help find them somewhere to live.
"As a council, we are facilitating more papakainga housing, and are working with Te Taiwhenua o Heretaunga to develop the country's second co-housing development in Flaxmere. We are also working closely with Housing New Zealand who are looking to develop their housing stock in Hastings, and with MSD to find more emergency housing over the winter so minimal people have to sleep in their cars."
