Gillot joined Bordeaux in 2011 and has helped the 2009 French champions recover after two disappointing seasons, leading them to a European qualifying place in his first year in charge.
"Francis and I are pleased to announce that we have found an agreement to extend his contract for two years," Bordeaux president Jean-Louis Triaud said.
"Francis managed to regenerate the squad and his personality fits this club," he added.
The 52-year-old Gillot, linked with several French clubs in as his contract was due to end next June, said the decision was easy to take.
"I did not hesitate. When the owner, the president and the management trust you, when the fans want you to stay, there's nothing to say," Gillot said.
Bordeaux are seventh in the Ligue 1 standings on 29 points at the halfway point of the 38-game season, nine behind leaders Paris St Germain.
They have qualified for the Europa League last 32 where they will face Dynamo Kiev.
President Triaud also said the club has submitted a long-term contract offer to striker Yoan Gouffran, whose current deal ends in June.
Gouffran, who scored 14 league goals last season, has netted seven in 18 appearances this term.
Meanwhile Bordeaux said they are still awaiting the return of Brazilian striker Jussie with the winter break coming to an end on Sunday with a Coupe de France match at Châteauroux.
Triaud said he had been delayed by family problems.
"The mother of Jussie had a problem on the way to the airport, or so he said," said Triaud.
"She could have broken her leg or something at the airport [from what he was saying]. He missed his plane. He was supposed to arrive today.
"We'll settle this with him on his return... if it was real, he could have found a less original explanation.
"Well, we are not convinced. He was asked to send a photo and we saw a leg in a cast - but I did not recognize his mother!"