The sale is set to make a profit of around £16 million to be disclosed in the second half of Kier’s financial year.
Around £2.2 million of the total comes from deferred profit following a financing in August 2004. The deal will give a return of around five times its original investment.
Hairmyres was one of Kier's first investments in a PFI project, which achieved financial close in March 1998. It is a district general hospital with a 24-hour accident and emergency department and 415 inpatient and day care beds.
The firm will announce its interim results for the six months to 31 December on 27 February.