The recording from United Airlines Flight 93 will be played in the sentencing trial of would-be al-Qaeda pilot Zacarias Moussaoui, who could face the death penalty for his role in the attacks.
The flight crashed into a field in Pennsylvania after passengers apparently fought back against the hijackers.
The hijackers are thought by US investigators to have been planning to crash the jet into the US Capitol.
Flight 93 had originally departed from Newark on the morning of September 11, bound for San Francisco. It changed direction after the hijacking and was just 20 minutes flying time from Washington when it crashed.
The flight is best known for one passenger's rallying cry "Let's roll," as he urged other passengers to try to retake the plane.
That was overheard over a mobile phone connection between a passenger and a family member on the ground.
The cockpit tape itself was played in private in April 2002 for the families of Flight 93 victims, but it has never been played in public.
At the time, family members told reporters that they heard yelling and screaming and muffled voices that were hard to identify.
The tape will be played in the trial
of Zacarias Moussaoui
Alice Hoglan, whose son, Mark Bingham, called her from the air before the plane crashed, said: "Listening to the tape confirmed for me that there was a heroic teamwork effort."
Although the recording is to be played in open court in the Moussaoui trial, it remains to be seen whether it and a transcript will be kept sealed from the general public.
Agreeing with a prosecution request to play the tape, Judge Leonie Brinkema said she was "also mindful that family members of the flight crew or passengers on Flight 93 may object to the voices of their loved ones being publicly revealed in this manner".
She said relatives would have until next Tuesday to advise her on whether they object to the general release of the material.
On Monday, the jury in the Moussaoui trial decided that the 37-year-old Frenchman was eligible for the death penalty for his role in the 2001 attacks.
The Pennsylvania crash site is
now a national memorial
Presenting its case, the prosecution had argued that Moussaoui's lies after he was detained in August 2001 facilitated the attacks.
In the sentencing phase of the trial, which begins on Thursday, the jury must decide whether Moussaoui will be executed or imprisoned for life without parole.
It is not yet clear when, during this second phase, the tape will be played.
As well as the playing of the recording, it has been reported that Rudolph Giuliani, the former New York City mayor, will give testimony for the prosecution.
A Hollywood film re-enacting the hijacking and final moments of Flight 93 is to be released later this month.