Leeds City Council has granted the construction of 32 homes at Bodmin Road in Middleton, and a separate proposal for 10 apartments next to Sunnyside Road in Bramley.
It comes after the the YEP last week reported that social housing provider Stonewater Ltd has applied to create 65 homes at Leeds City College's former Horsforth Campus on Calverley Lane, a further education facility that closed in 2017.
Reuben Young, director of housing campaign PricedOut, said: "We have a huge shortage of affordable housing in England, and these new developments will help the people of Leeds by housing those who struggle to access market housing and by bringing rents and prices down for everyone."
The Middleton plan, submitted by ESH Construction, relates to vacant land once occupied by two care homes.
There would be a mixture of flats and houses, with 23 units intended for shared ownership and nine for affordable rent.
In a report, Leeds City Council's chief planning officer Tim Hill wrote that it will "provide a much needed and welcome contribution to the local housing which generally has a significant amount of much older social and in some parts poor quality privately owned housing stock".
In Bramley, Loroc Architects and Leeds Federated Housing Association (LFHA) will develop the 10 apartments.
LFHA is aiming to build 1,500 homes over ten years to help address the need for affordable housing across the the area, and the latest approvals in planning applications for affordable homes come after a range of other such sites have been proposed or built in the city.
A mix of mix of two-, three- and four-bedroom houses for social rent and shared ownership are planned in Horsforth, while Chapeltown Cohousing is developing 29 new affordable, low-energy homes with shared facilities and gardens.