"Although the scene on board is chaotic and blurred, and no individual person can be identified, the authenticity of the video is beyond doubt," Bild wrote.
The paper reports that the video was found on an undamaged digital storage device at the scene of the crash.
Recorded from a vantage point at the rear of the plane, it shows that the passengers were screaming in the aircraft's final moments.
The words "my God" can be heard in several languages.
The video also appears to confirm French prosecutors' evaluation of the cockpit data recorder, with three metallic blows clearly audible – matching the theory that the captain of the flight tried to break down the cockpit door with an axe.
Shortly before the end of the video, part of the plane appears to strike the mountain, as the cabin jolts to one side.
More screams are briefly heard before the video ends.
"I think it's very unlikely that a smartphone would survive such a crash," Dirk Lorenz of the Product Testing Foundation (Stiftung Warentest) told Bild.
"But the memory cards inside them can be very resilient. Even if a phone is smashed to pieces, the memory card could survive."
However, French police official Lieutenant-Colonel Jean-Marc Menichini denied that investigators had found mobile phone footage at the crash site, telling CNN that the reports were "completely wrong" and "unwarranted".
Marseille prosecutor Brice Robin said anyone with footage "must hand it over immediately to investigators".
Flight school knew of co-pilot depression
Meanwhile, Lufthansa released a statement on Tuesday saying that co-pilot Andreas Lubitz, suspected of deliberately steering the aircraft into the French Alps, reported his pre-existing depression to their flight school.
He emailed the flight school with medical records detailing a "serious depressive episode that has now passed" in 2009, shortly after returning to his training following a break he took for psychiatric treatment.
The airline said it had passed the information to state prosecutors in Düsseldorf.