The grants from the Housing Infrastructure Fund will support the development of new housing at land to the east of Otley and at Roundhay Road in Chapeltown.
Together the schemes will result in the creation of 614 new homes, of which more than 200 will be affordable housing.
The bid for the funding was made by Leeds City Council working with the developers for each site.
Coun Richard Lewis, executive member for regeneration, transport and planning, said: “These projects are different in many ways but demonstrate the breadth of our approach to delivering planned housing growth, whilst recognising the diversity of needs and aspirations across the whole district."
He said the council would be working with the government in the coming months to finalise the details of each of the schemes.
The Roundhay Road development is being led by Unity Housing Association and Chapeltown Co-housing (ChaCo).
It benefit from a grant of Â£990,000 to remediate the site and to build affordable apartments for over-55s alongside an innovative project led by local people to create a co-housing scheme along with self-build opportunities.
ChaCo chairman Bill Phelps said: “This is great news for Leeds, for Chapeltown and for community-led housing.
"We are delighted that the council has secured this grant approval, which helps make the site economically viable, and will support Chapeltown Co-housing in its ambitious plans to create affordable community-led homes."
Wayne Noteman, regeneration director at Unity Homes and Enterprise, added: “It’s been a long journey to get to this point. We and ChaCo are almost ready to commence building a scheme, that when complete in late 2019, will leave a lasting legacy in the community."
Meanwhile, developer Persimmon Homes is working with other landowners in Otley and playing a leading role in bringing forward the critical infrastructure proposals.
The site in question is a long-standing part of the city’s agreed planning strategy and is allocated for the development of 550 new homes as well as a new primary school, employment uses and green space.
Funding of Â£6.3m will support construction of the East of Otley Relief Road that will, subject to planning permissions, provide an eastern bypass to relieve relieve traffic pressure on Otley town centre and allow construction of the additional housing.
Chris Hull, land director for Persimmon Homes West Yorkshire, said: “We’re delighted to hear the news that we’ve been successful in our joint bid to secure HIF Marginal Viability Funding for the highways infrastructure that will unlock the east of Otley site.
We look forward to continuing our ongoing work with Leeds City Council to bring forward the construction of the relief road as well delivering much-needed housing in an area where homes are in high demand.”
The council is also awaiting the outcome of a further major bid under the Housing Infrastructure Fund that could support the delivery of over 16,500 new homes in the city centre.