Thomas Vale currently employs over 700 people and is on track for a £200m annual turnover.
The deal follows similar takeovers by Bouygues of regional contractors Warings, Leadbitter and Denne.
Thomas Vale will be bought via its subsidiary Bouygues Bâtiment International subject to European Commission approval.
Bouygues is looking to grow the Thomas Vale business and compete for larger contracts across the Midlands.