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The transition support service is expected to help about 3000 young people over the next four years, she said.
Oranga Tamariki has been tasked with building the service, which will employ 175 new specialist staff and make 60 supported accommodation facilities available by year four.
There will be $25m allocated to supporting young people to live with their caregiver beyond the age of 18, and $9m to help the transition from care to independence, up to the age of 25.
Ms Martin said young people who have been in the care of youth justice systems have had a difficult start to life and it was wrong that support for them ended when they turn 18.
"Teenagers leaving care should have the right to expect what any young person would want - knowing there is someone to turn to if they need help; a warm bed to sleep in; some help and encouragement when it is needed.
"This service will provide that, both by allowing young people to stay longer with their caregivers and providing specialised transitions support workers whose job is to help this group."
The minister said that young people who have left the state's care and protection have in the past ended up with worse outcomes in nearly every key area including health, housing and incomes.
Young people were engaged in the design of the transition service, which will largely be provided by non-governmental organisations (NGOs), iwi and Māori organisations.
"This was a deliberate decision. The service is voluntary and we want young people to engage with it. Oranga Tamariki hasn't generally worked with 18-25 year olds, but its community partners already have a youth focus and capability to work with this group."
Making the investment now reduced the risk of personal cost to the young people and would help break the cycle of families needing state care.
Nearly 30 percent of children in care have parents who had also been in care, Ms Martin said.
The new services include:
- 175 new specialist transition support staff by year four providing day-to-day support to individual young people as they transition out of care
- 60 supported accommodation places by year four for young people who need a stepping stone to make a successful transition to independent living
- $25m over four years to support arrangements for young people to continue to live with their caregiver beyond the age of 18
- $9m over four years to provide advice and assistance to individual young people transitioning from care to independence, up to the age of 25.