The Sunday Times reported that the tape, with no audio, shows the two al-Qaeda hijackers reading two documents marked as wills in Arabic.
Atta was the purported leader of the September 11 attacks, piloting American Airlines Flight 11, which crashed into the north tower of the World Trade Center. Jarrah flew United Airlines Flight 93, which crashed in a field in Pennsylvania after passengers on the plane revolted against their hijackers.
The Times said the video was filmed January 18, 2000, and had been authenticated by US authorities. The newspaper did not say how it had obtained the tape, which it would release at noon (1100 GMT) Sunday.
The tape also shows clips of al-Qaeda leader Osama bin Laden addressing a crowd of 100 members near Kandahar, Afghanistan, on January 8, 2000, the paper said.
