The fund will be used to either help set up locally-led schemes or expand those currently in use, the Ministry of Housing Communities and Local Government (MHCLG) said.
These schemes will be tailored to match the needs of each local area’s residents and landlords.
This could involve councils providing financial support to help those to access or maintain their tenancies, such as paying deposits for the tenancy or rent payments.
Alternatively, some schemes may involve the council managing the property on the landlord’s behalf.
The minimum tenancy or existing tenancy supported by the schemes will be a period of 12 months.
Up to £5m is available for bids for the 2018 to 2019 financial year with £15m available for the 2019 to 2020 financial year.
Duty to refer
The fund is based on a previous programme by homelessness charity Crisis which ran from 2010 until 2014, backed by £11m in funding from the government.
It supported more than 153 schemes across the sector, creating 8,000 tenancies over four years with 90% of these schemes lasting beyond six months.
The fund comes alongside a new duty for key public bodies such as prisons, job centres and NHS Trusts to refer people at risk to their local housing authority.
Brokenshire said the private rental sector could be an important part of helping to reduce homelessness.
“It is vital we give people facing homelessness a route out of it and a chance to rebuild their lives. The private rented sector has an important role in this,” he said.
“This £20m fund will allow councils to put in place vital new schemes so those at risk will have the support to secure their own tenancy.
“It is just one part of the wide-ranging work we are doing to help tackle all forms of homelessness, including our Rough Sleeping Strategy as we ensure more homes are made available for those in need,” he added.