The 32-year-old has won 10 caps for France and made more than 100 Gloucester first team appearances.
Azam said: "I am lucky to have been involved in a number of squads at Gloucester, but the one (head coach) Dean Ryan is assembling at the present time is the best I have seen.
"To have the opportunity to be part of that for another two years is fantastic.
"Our current position in the Premiership shows the potential of this squad. As we continue to develop, I really believe we can challenge consistently for the major trophies."
Gloucester recently signed England international hooker Andy Titterrell from Sale Sharks, although uncertainty surrounds the Kingsholm future of their former Wales hooker Mefin Davies, who has been linked with a move to Leicester.