Worsley, 34, who won 78 England caps and was part of the 2003 World Cup-winning squad, was forced to retire in November after failing to recover from a neck injury.
He was approached by Bordeaux-Begles president Laurent Marti for his first professional coaching role on the advice of new general manager Raphael Ibanez, who Worsley played alongside for Wasps.
Former France hooker Ibanez told the Bordeaux website: "He is someone who is hugely competent.
"I played with him for five years at Wasps and could see his qualities as a defender and the ideas he had concerning that sector of the game."
Bordeaux-Begles finished an impressive eighth in the Top 14 this term, having been tipped for relegation.