The construction giant acquired Fitzgerald last year when it bought Thomas Vale Group, which owned the civil engineering business.
Bouygues said the business, which was founded in Birmingham in 1948, did not fit with its focus on building work in the UK.
The management buy-out was led by Nick Coley, current managing director.
He said: “Fitzgerald is a £24m company, employing over 100 local people.
“I am delighted to have completed the acquisition of the company and am confident that as an independent company we will be able to offer an even greater top-down commitment and focus to our clients.
“It will also present us with many opportunities to deliver business growth and enhance client care and project delivery.
“It is a great achievement to be celebrating our 65th anniversary and the acquisition will present a new chapter in our history.”
Madani Sow, chairman of Bouygues UK, said: “The Fitzgerald management team has developed the business into a strong player, with a proven track record in its sector.
“I am very pleased that we have been able to divest the business to Nick and I wish him every success for the future”