The plane's flight data recorder was pulled from the water Monday and will be analyzed by authorities.
Mardjono Siswosuwarno, the chief investigator with Indonesia's National Transportation Safety Committee, said the cockpit voice recorder has not yet been retrieved but its position has been determined and it will be "a matter of hours" until its brought to the surface.
Search crews hoisted the tail of the jet from the sea on Saturday, but the black boxes were not found inside.
However, searchers detected a ping-like sound that was believed to have been coming from the black boxes.
The black boxes, which feature cockpit voice and flight data recordings, may have dislodged from the plane's tail when it crashed into the sea on Dec. 28, Indonesian military commander Gen. Moeldoko told The Associated Press.
The discovery of the plane's tail last week was a major breakthrough in the slow-moving search that has been hampered by seasonal rains, choppy seas, and blinding silt from river runoff.
At this point, nearly 50 bodies have been recovered from the crash, which killed 162 people.
Get real-time updates as this story unfolds. To start, just "star" this story in ABC News' phone app. Download ABC News for iPhone here or ABC News for Android here. To be notified about our live weekend digital reports, tap here.