This week the council will take over the homes at Connect at Halfway, which are a mix of two, three and four bedroom properties, and give them to waiting residents.
It was built by Taylor Whimpey, who are helping them deliver their New Homes Delivery Plan.
Over the next five years the council aim to provide 1,600 new homes across the city to meet growing demand for affordable places to live.
Ian Thomson, land director at Taylor Wimpey Yorkshire, said: “This is a fantastic milestone for the development team, as delivering much-needed affordable homes is something we’re committed to and really proud of.
“As well as our continuous programme of engagement with local communities, working with the city council is a key way for us to give back to the communities in which we build.
“We hope the future residents of these properties are all very happy at Connect at Halfway.”
The next five years will see them try to fullfill new homes targets by acquiring new homes and building affordable properties with developers.
Councillor Jim Steinke, cabinet member for neighbourhoods and community safety, said: “This is good news for our city because these new council homes will help us to meet the higher than ever demand for affordable social housing. They will be in the right locations, well insulated and affordable.
"We are pleased to be working with Taylor Wimpey to deliver them and it’s particularly good to see the arrival of these new, welcoming properties . We will continue with our commitment to provide everyone with a safe, affordable and quality home.
“One of the most important parts of our work will be the discussions we have with our tenants and residents so that they can tell us what kind of housing best meets their needs. Of course, as part of this it will be important for the Government to give councils across the country what they need too so that they can build truly affordable homes for social rent.”