The Arabic satellite television channel al-Jazeera began broadcasting excerpts of a videotape featuring the voice on Monday but the full list of the hijackers was only given in a version shown on Tuesday.
The fate of Bin Laden, who is accused of masterminding the attacks, is still unknown.
The BBC's Jim Muir says the video adds up to the most comprehensive, illustrated admission by al-Qaeda that it indeed perpetrated of the attack which is glorified so vividly on the tape.
Timed to coincide with the anniversary, it is clearly meant to send the message that al-Qaeda is still in business, our correspondent says.
Al-Jazeera showed a fuller version of the tape on Tuesday but it still did not feature any video of Bin Laden apart from archive footage.
The identity of the speaker cannot be independently confirmed and it is unclear when the tape was recorded.
But correspondents agree that the voice sounds very similar to previous recordings of the al-Qaeda leader.
Full nineteen
Tuesday's recording lists all 19 men identified by US investigators as those who hijacked and crashed civilian airliners into New York, Washington and rural Pennsylvania.
In the initial excerpts shown by the TV, only four ringleaders are named by the voice: Mohammed Atta, Marwan al-Shehhi, Hani Hanjour and Ziad Jarrah.
Speaking in Arabic, the voice describes the hijackers as "men who changed the course of history" and "torpedoed decades of scheming by the crusaders [ie Christians] and their agent rulers in the region".
The full recording gives the names and places of birth of each and every one of the 19, praising them for Islamic piety.
The broadcast features pictures of the 19 and old video of Bin Laden, as well as video of what appear to be some of the hijackers training in Afghanistan.
The men are shown reading flight manuals and studying maps, one of which is of the Washington DC area.
Trained by Bin Laden
Included on the tape is a farewell message being read out by hijacker Abdulaziz Al-Omari - said by the FBI to have been on the first plane to fly into New York's World Trade Center.
After condemning America and Israel, Al-Omari thanks Bin Laden for his guidance:
"May God reward all those who trained me to tread this path and contributed to this great action. I would like to particularly mention mujahid leader Sheikh Osama Bin Laden..."
Al-Jazeera says the tape was shot in the southern Afghan town of Kandahar and supplied by a mysterious company named "Sahab".
Al-Qaeda interview
The same channel has broadcast previous statements by Bin Laden.
It also reported over the weekend that one of its correspondents had interviewed two leading al-Qaeda fugitives in June.
They reportedly told al-Jazeera that al-Qaeda initially planned to fly hijacked jets into nuclear installations - rather than the World Trade Center and the Pentagon.
The US Congress was the fourth American landmark on al-Qaeda's 11 September hit list, the correspondent added.
This interview is due to be broadcast in full by the channel on Thursday.