The deal will see 20 staff transfer to Kier together with contracts in progress worth £15m and a pipeline of potential future work valued at approximately £20m.
The business will operate from Aberdeen as part of Kier Group’s regional network of UK construction businesses.
It will initially be known as Kier Milne.
Kier Group chief executive Paul Sheffield said: “I am delighted that this acquisition has concluded successfully and welcome the Stewart Milne team to Kier.
“We are keen to grow the business and our new base in Aberdeen should provide further, good opportunities for expansion in Scotland and the North-East.”
The Enquirer first revealed talks were taking place in March.
Stewart Milne said at the time: “Should this go ahead it would allow the Stewart Milne Group to focus on expanding and developing its successful house building and timber frame operations across the UK.”
Turnover at Milne’s construction division grew to £30.1m from £22.3m in the year to June 2011 from a group turnover of £239.4m.