Bouygues now owns a majority stake in the £400m turnover contractor through its subsidiary Bouygues Batiment International and current chief executive Bob Rendell will remain in his role.
Heijmans has been looking to sell the business since April 2009 after announcing it would concentrate on the Dutch market.
The Leadbitter Group also includes Denne and bosses at the firm believe the backing of Bouygues will allow the firm to flourish.
Bob Rendell said: “This is a very exciting time for the Leadbitter Group and its employees.
“The resources and strength which will now be available to our Group will place us in a very enviable position and enable us to influence and take advantage of the new private investment models that are emerging in our core sectors, including mixed tenure regeneration and zero grant developments.
“I am confident that we are now extremely well placed to capture further market share in a number of our key areas”.
Olivier-Marie Racine, Chief Executive and Chairman of Bouygues Bâtiment International, said: “This agreement in conjunction with the Leadbitter Group management team is an excellent illustration of our development strategy in the most buoyant regions of England.”