The residential division of the company, Kier Living, will design and build 71 properties across three sites with a total value of £10 million.
A total of 25 homes will be built at the Garnets in Hunslet, while 24 properties will be delivered at the Broadleas in Bramley.
Plans for the former Whinmoor pub site in Swarcliffe are yet to be drawn up. However, proposals are in place to build 22 houses.
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The construction value of each site is £3.5m, £3.4m and £3m.
The three sites are the next phase of the council house growth programme, which will see around 1,000 new council homes built over the next three years.
While Kier will help finalise the look and design of the homes, each will conform to the Leeds Standard.
The council is now working with Kier to be in contract for the Broadleas and Garnets sites in spring 2016.
Jon Rukin operations director at Kier, said: "Kier is pleased to have been selected for this exciting opportunity to deliver much needed affordable homes and to be an integral part in the delivery of the council house growth programme in Leeds.
"The council's innovation in the procurement process allows us to become involved much earlier in the design and development stages and to use our breadth of capability to bring these projects to site."
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