The money will be made available to remove aluminium composite material (ACM) cladding from around 170 buildings across the UK.
It comes after almost two years of inaction from some building owners.
Campaigners welcomed the news, with Grenfell United, a group of survivors and the bereaved, saying it offered hope to people feeling at risk at home.
Seventy-two people died during and after the fire at the 24-storey Grenfell Tower in London on June 14, 2017.
The Ministry established the Building Safety Programme after the tragedy to cover residential buildings over 18 metres, including hotels.
In data released in March, the Government reported that at least 14, and potentially up to 30 buildings in Yorkshire - between six and 10 in Leeds and Sheffield each and between one and five in Kirklees and Bradford each - had ACM cladding systems unlikely to meet its Building Regulations.
Leeds City Council subsequently named six buildings that then had Grenfell-style cladding as 20:20 House in Skinner Lane, City Island Phase 2, Waterside Apartments Aruba & Montagu in Gotts Road, the Park Plaza Hotel in Boar Lane, Quay One in Neptune Street, Skyline Apartments in St Peter’s Square and 1 Brewery Wharf in Waterloo Street
Removal works were due to be completed later this year and those at City Island were expected to start early 2020.
Bradford Council also named Landmark House in Broadway and Appleton Point in Hamm Strasse as buildings that had Grenfell-style cladding.
Works at the former building were understood to be under way last year.
Sheffield and Kirklees councils are yet to respond to a request made today for details of other buildings.
“Although temporary safety measures are in place to ensure people living in these buildings are safe right now, too many building owners are touting them as a solution rather than getting on with the job of making a permanent fix,” said Housing Minister Kit Malthouse MP.
Grenfell United said the announcement “offers hope to people in dangerous blocks that the nightmare they have been living for nearly two years is almost over”.
Latest Government figures show that 166 private buildings out of 176 identified nationally with the cladding after the fire in June 2017 have yet to start removing the material.
Building owners will be able to register for the fund by early July, and have three months to claim the funds.