The funding is the first tranche of the £400m pledged by prime minister Theresa May earlier this year to cover the costs of removing unsafe aluminium composite material (ACM) cladding from council and housing association tower blocks after the Grenfell Tower fire.
The money will be allocated to 12 local authorities and 31 housing associations, covering 135 buildings.
The Ministry of Housing, Communities and Local Government (MHCLG) has received applications for funds for 159 buildings.
It rejected 12 that were not eligible for funding because the buildings are owned by commercial freeholders, are under the 18 m height limit, or the cladding is not ACM.
The government has requested more information on 12 other applications and will review these, and any others it receives, in December.
Housing secretary James Brokenshire said: "There is nothing more important than ensuring people are safe in their homes and that is why I am pleased that £400m funding has started to be released.
"We are doing the right thing by residents and fully funding the replacement of unsafe ACM cladding in social housing buildings 18 m or above."
The cash grants will be payable in two tranches that are expected to be made in 2018-19 and 2019-20, the government said.
It will pay 80% of the estimated costs upfront "to ensure work can start with no delay", and the remaining 20% once work has been completed and the final costs are known.
According to MHCLG figures from September, ACM cladding has been found on 159 social-sector residential tower blocks since June 2017, when a fire broke out in the 24-storey Grenfell Tower block of flats in west London.
The government said that cladding on 76% of these buildings has either been replaced (22) or is in the process of being removed (99). Corrective action plans are in place for the remaining 38 buildings.
There are also 295 private-sector structures that are in clad in ACM, including 205 residential blocks. Statistics show that replacement work has finished on just ten of these buildings and remediation work is underway on a further 26.
Brokenshire added said: "In the private sector, I want to see landlords protect leaseholders from these costs. I am pleased that a number have stepped forward to do so [-¦] However, there are some who are not engaging in this process. If they don't I have ruled nothing out."
