The video, which the British government had previously not allowed Hull's family to see, was leaked to The Sun newspaper on Tuesday.
Following the leak, the US military approved the release of the gun camera video to both the British coroner and the family of the victim, a military spokesman said.
In the video, one pilot in an A-10 attack jet can be heard saying "I'm going to be sick" and "we're in jail, dude", after he realises he mistakenly opened fire twice on a convoy of light British tanks, killing one soldier, later identified as Hull.
Another pilot is later heard weeping and says: "I'm dead."
Washington gave the video to British authorities, but refused to allow it to be shown in public, saying it might contain security secrets. The British government said it could not release it without US permission.
Geoff Webb, clerk to coroner Walker, told Reuters the video would now become evidence in court.
He said: "The coroner thinks the video is central to the inquest. Because it is in the public domain it can be used."
Friendly fire has been an issue for both countries since the first Gulf war in 1991, when nine British servicemen were killed in a mistaken attack by US aircraft.
Precautions have since been taken - orange panels were fitted to allied vehicles to alert pilots during the 2003 invasion. The pilots on the tape can be heard concluding the panels were "orange rocket launchers" before opening fire.
Washington's refusal to allow the video to be shown angered the family and British soldiers' groups, who accused the Us of trying to cover up embarrassing details.
Hull's family says they were initially told no such video existed. The British defence ministry said it had told the family that there was evidence that had not been made public.
Margaret Beckett, Britain's foreign secretary, said during a visit to Jerusalem, after the video was aired: "Obviously, both we and the US are keen to understand what has happened here."
Washington has refused to allow its servicemen to be sent to Britain to testify in cases involving the deaths of British troops. British officials say they would be willing to send British troops to the US under similar circumstances.
|The US has approved the release of the |
leaked video to Hull's family [AP]
David Johnson, deputy chief of mission at the US embassy in London, said Washington was not trying to hide the truth of the incident but has its own procedures for investigations. It was reviewing whether the cockpit video could be declassified.
Johnson told BBC radio: "If indeed it can be declassified, of course it will be."
Lieutenant-Colonel Daniel King, a spokesman for the US central command, on Tuesday said lawyers for the command approved the request for the release of the video, which had already been leaked.
King said: "The legal arm of Centcom has authorised the release of the footage to the family and the coroner."