Balfour Beatty chief executive Mike Welton said the deal expanded the group's infrastructure services businesses.
He said: "The acquisition provides us with a quality business, which has a significant opportunity to grow with the fast-expanding requirements for maintaining and upgrading utility networks." In the year ending 31 March, Kennedy had sales of almost £73m and an operating profit of £4.5m.
It has a forward order book in excess of £200m, according to Balfour Beatty.
The firm will be bought from its current and past management and from clients of Aberdeen Murray Johnstone Private Equity, with whom a management buyout was executed in 1997.
Kennedy's customers include Transco, Southwest Water, United Utilities, Severn Trent Water, Yorkshire Water and the Scottish water authorities.
Brearly, who starts her new job in January, will join from Railway Safety, the company formed from Railtrack's safety and standards directorate.
She will report directly to chief executive Mike Welton.