The company will help build 2,300 Private Rented Sector (PRS) properties across seven neighbourhoods in the city.
SHC is a partnership between Sheffield Council, Keepmoat and Great Places Housing Group.
Sigma and SHC will work together over the next three years to deliver two, three and four bedroom homes for private rent.
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Graham Barnet, Chief Executive of Sigma, said: "Following the expansion of our PRS programme with Gatehouse to 10,000 new rental homes, I am delighted to be announcing this major agreement with Sheffield Housing Company Limited for the delivery of new PRS homes across Sheffield.
"The agreement is another major step forward as we move ahead with our plans to establish, with our partners, one of the largest PRS platforms in the UK, focusing on the regions outside London."
Tom Fenton, Project Director with SHC, added: "This is a high profile agreement with which we are proud to be associated."
(LM)
