The deal is conditional on Kier shareholders’ approval at a General Meeting scheduled for early next month.
Kier will receive £110m in cash on completion of the sale which is expected before mid-June.
Hands and his newly formed company Foster BidCo have paid a non-refundable deposit of £40m to guarantee the deal.
Kier will use the proceeds to reduce group debts which stood at around £436m earlier this year.
The contractor said: “The sale of Kier Living is another step in the management’s strategy to simplify the group and to create a strong, resilient and flexible balance sheet, providing the Group’s clients, customers, suppliers and other stakeholders with greater confidence in Kier as a counterparty.”
It added that a potential equity raise is still a possibility.
Kier publishes its interim financial results for the six months ended 31 December 2020 next week.
Andrew Davies, Kier Group Chief Executive Officer said: “The actions we have taken over the last two years have created a strong operational platform for sustainable profitable growth and free cash flow.
“The disposal of Kier Living delivers another key milestone in the Group’s strategy to simplify the business and strengthen its balance sheet.”