The new test, which will replace the current smear test, is a simple and quick swab that women can choose to do themselves.
"This will help to reduce the barriers to getting screened," Verrall said.
The announcement will come as welcome news to advocates, who have been calling for the Government to fund self-testing kits for some time.
Verrall said initial modelling predicted the move to HPV screenings would prevent about 400 cervical cancers over 17 years.
"It will save around 138 lives," Verrall told reporters this morning, adding that a third of those cases prevented and lives saved would be Māori, Verrall said.
The change will come into effect in 2023.
The funding comes after Cabinet Minister Kiri Allan last month revealed she has cervical cancer and has just a 13 per cent chance of survival.
Verrall said she spoke to Allan about the announcement last night: "She's just so excited about the change."
She said the Government had been working on the programme for "a long time".
"I've been a doctor for a long time and met many, many women affected by cervical and breast cancer. I think today's announcement is for all of them."
In addition to the new HPV test, the Government also announced that almost 300,000 extra women will be eligible for potentially life-saving free breast scans because of a $55 million upgrade of the Government's aged IT systems.
The funding is part of this month's Budget and is one of the first funding initiatives to be announced.
It will come as welcome news to advocates, who have been pushing the Government to expand the number of women who get the free scan.
The money for the new IT system will help proactivity identify and enrol eligible women into the Government's free mammography screening programme.
The existing system operates as an "opt-in" model, whereby women choose to enrol for breast screening via their GP or by calling a 0800 number.
But this model relies on women knowing they are eligible for free breast screening and making an appointment themselves.
Associate Health Minister Ayesha Verrall said the current "ageing" IT system put the whole programme at risk.
"It lacks the flexibility to be easily upgraded to meet the needs of the community, and is no longer supported well by vendors."
The national breast screening programme, Breast Screen Aotearoa (BSA), provides free mammography screening every two years to women aged 45 to 69 who have no symptoms of breast cancer.
The Government will spend $55.6m on a major technology upgrade, which will better equip the system to identify women who are not currently being screened.
Verrall said about 271,000 women were in this category.
The new system will directly invite those women who would have otherwise missed out by running targeted campaigns.
It will mean when women are offered an appointment, they can choose to participate or ask to opt out.
"With more Māori and Pacific women dying from breast cancer compared with non-Māori and non-Pacific women, the new system will allow BSA to identify priority group women who may not already be part of the programme."
Each year in New Zealand, about 3200 people are diagnosed with breast cancer and about 600 die from breast cancer.
Ah-Leen Rayner, chief executive of Breast Cancer Foundation NZ, said this is an excellent step forward.
"With more than 650 Kiwi women still dying from breast cancer every year, and with wāhine Māori being 65 per cent more likely to die than Pākehā, knowing who's missing out on mammograms is vital."
In addition to the $55m in upgrading the IT system, Verrall announced a further $10m to be spent on catching up on providing those who missed their screenings because of Covid-19 lockdowns with a free scan.
