Gourvennac had been relieved of his duties on January 18, after Bordeaux slumped to a 2-0 home defeat at the hands of Caen.
That loss, the club's 10th in the last 15 games, leaves Bordeaux rooted in mid-table having seen a positive start to the 2017-18 season go up in smoke.
They currently lie in 11th, with caretaker coach Eric Bedouet leading the side to a 1-0 victory over Nantes on Saturday.
Now, they have turned to former Chelsea star Poyet in a bid to revive their fading fortunes.
"Bordeaux have named Gustavo Poyet to the post of club trainer," the club confirmed on their Twitter account.
"He will be accompanied by Mauricio Taricco and Fernando Menegazzo as his assistants."
Poyet, 50, was last employed in China by Shanghai Shenhua, where he resigned in September after less than a year in charge following a disappointing set of results.