The schemes were being considered by the agency after severe cuts to its budget in May and July.
44 out of 74 Kickstart schemes will go ahead while 61 of 91 LANB projects also got funding.
The HCA estimates this could mean over 5,400 homes are built.
Sir Bob Kerslake, chief executive of the HCA, said: “Following a period of uncertainty, I am pleased to be able to firm up the position with our partners. Our allocations, based firmly on discussions with partners, have maximised the supply of affordable housing and value for money, meeting local priorities.”