Rodriguez approved the destruction of the tapes due to fears that their release could have a "devastating" effect on the CIA if they were to be somehow made public.
The correspondence shows that Goss "agreed" with the move, but an investigation by the New York Times newspaper said that neither he nor the CIA's top lawyer were actually told of it before it happened, which displeased Goss.
CIA officials were shown in the emails to be immediately concerned that they had made a mistake in destroying the tapes.
The documents also convey that Harriet Miers, the White House counsel to George W Bush, the former president, was deeply unhappy when informed of the tapes' destruction two days after the event.
As Goss was not informed of the destruction of the tapes before it happened, the emails do not implicate him in the approval of their obliteration.
Gross has not spoken publically on the events.
Current and former intelligence agents have said that Goss did not approve of the destruction, which took place in Bangkok, the Thai captial, and was angry when told about it.
John Durham, a prosecutor investigating whether any crime was committed, said: "These documents provide further evidence that senior CIA officials were willing to risk being prosecuted for obstruction of justice in order to avoid being prosecuted for torture."
Goss, a Republican politician from Florida, was appointed by Bush to be head of the CIA from between 2004 to 2006.
The Justice Department released the correspondence under a Freedom of Information Act request filed by the American Civil Liberties Union (ACLU).
Ben Wizner, an ACLU lawyer, said. "If the Department of Justice fails to hold these officials accountable, they will have succeeded in their cover-up."