Sagnol takes charge at the Stade Chaban Delmas following a spell at the helm of France's Under-21 side.
The 37-year-old has signed a three-year contract that will keep him with the six-time French champions until 2017.
The appointment comes after Gillot, who had previously spent three years as head coach, announced that he would not be extending his deal with Bordeaux.
Bordeaux won the Coupe de France in 2012-13 under Gillot's leadership and have not finished outside of the top half since 2005.
However, a seventh-placed finish this term was not enough to secure UEFA Europa League football for the third straight season and Sagnol will likely be tasked with returning Bordeaux to continental competition as he takes his first foray into club coaching.
