A total of eight new two-bedroom homes are being built at the former Lord Cardigan pub site in Bramley.
The roof on the first row of three townhouses is almost complete, while groundworks and foundations for the second row of fives homes are now finished.
The council has agreed to purchase the energy efficient properties from RDF as part of its plans to provide 1,000 new council homes.
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Cllr Debra Coupar said: "We need to be innovative in how we provide much needed council homes. As well as building our own homes, if we can purchase new homes from developers in areas where demand exceeds supply then we'll make that investment.
"It's great to see work cracking on at such a pace and as always, we're looking forward to welcoming tenants to their new homes."
RDF Building Services MD Michael Brearey added: "We are delighted to be involved with this development which is local to our head office having delivered similar projects across the Yorkshire region and beyond."
(LM/CD)
