The Boeing 737 crashed on Jan. 25, just minutes after takeoff from Beirut during a thunderstorm. All 90 people on board died.
The plane's data flight recorder was retrieved among the plane's wreckage last week and was flown to France for analysis.
Part of the cockpit voice recorder was retrieved in the same area last Wednesday, but officials said it was missing its memory voice recorder.
An army statement said that recorder was retrieved Tuesday.
Both black boxes will be analyzed by BEA, a French agency that specializes in assisting with technical investigations of air crashes.