The job of assessing housing need is being moved from Housing NZ to the Ministry of Social Development.
Mr English suggested that possible private providers would include organisations such as the Salvation Army, iwi groups and the Presbyterian Church.
He said it was better to integrate housing provision with organisations that also provided support for people with disabilities and social problems such as drug and alcohol problems and family dysfunction.
The new system will start small, and the cost will be capped at $30 million over four years. But once it is established, it will be able to be easily expanded.
The changes may not meet much opposition from housing activists - many are part of community housing groups and support having more control over social housing.
Among the welfare reform measures is a provision to hire 354 new staff for more intensive case management of beneficiaries - work which could be contracted to out to private services.
Housing Minister Nick Smith said other social housing providers would be able to access the income-related rent subsidy currently only available to Housing New Zealand.
"The Government recognises that community housing providers such as churches NGOs, disability providers and local trusts are very good at providing a comprehensive wrap-around services for their clients."
The bill also allows for reviewable tenancies to be extended to all Housing New Zealand tenants.
"We have more than 4000 sate house tenants paying market rents, some of whom are on high incomes. This policy is about freeing up those homes for more needy families.
"Reviewable tenancies is budgeted to result in 1000 tenants in 2015/16 and 2000 tenants in 2016/17 being supported into housing independence.
Labour's housing spokeswoman Moana Mackey said the bill signalled the beginning of the end for Housing New Zealand.
"Too many families in this country don't have the stability that Phil Heatley and Dr Nick Smith take for granted.
"We have one department in New Zealand that is able to provide that stability and that is Housing New Zealand," Ms Mackey said.
Dr Smith said the changes built on the Government's $139 million investment through the Social Housing Fund and sit alongside Housing New Zealand's record $2.9 billion investment over three years on new builds, housing extensions, insulation, earthquake repairs, and maintenance.
