The scheme, launched by the department for communities and local government, will involve councils, developers and housing associations bidding for a share of the cash.
Most of the funding (£30m) has been set aside for viability assessments, planning and community engagement.
The £32m will be added to a £140m fund announced in January, which was set up to cover the cost of buying land, demolishing existing buildings and initial construction works, among other things. The rest will be spent on new staff and consultancy workers for local authorities.
The government said it intends to build thousands of new homes over the next decade through the initiative, and that it will also be giving councils and others advice on how to re-build estates.
Communities secretary Sajid Javid said: "Rundown estates offer huge potential to become new thriving communities providing homes, jobs and opportunities and places that work for everyone.
"That's why we're determined to ensure the success of regeneration projects through the national strategy to transform the lives of thousands of people by delivering better homes in better estates."