The houses, all for social rent, are being delivered on behalf of South Lanarkshire Council as part of a 163-unit mixed tenure development.
The homes will be added to the council's housing stock when completed and are part of the recently announced ambitious plans to provide 1,300 additional homes by 2027.
Chair of the council's Housing and Technical Resources Committee, Councillor Davie McLachlan, said: "It's fantastic news that we are continuing to make progress in improving the availability of high-quality social housing across South Lanarkshire.
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"When complete, these homes will be a welcome addition to the council housing stock and help us meet our target of 1,300 additional homes by 2027.
"The important thing is that we are making a difference by providing more affordable social housing, of a variety that meets the needs of local people while maintaining affordability and value for money."
Sarah Freel, Partnerships Manager for Lovell, said: "Glow Garren is one of our most important sites in Scotland, providing the right mix of housing needed for the local area to grow and thrive in the future.
"As part of that, I am delighted we are working with South Lanarkshire Council to deliver 40 high-quality homes for social rent that will provide housing for individuals and families.
"Partnership working is the key to providing the homes Scotland needs and Lovell are one of the pioneers of an effective approach of working with both councils and housing associations across the country.
"I can't wait to see these homes completed and families move in, adding to the richness of the local community."
Acquisition of the units will be partly funded from the Scottish Government grant for more homes.
