The prime minister gave his backing to Hunt just minutes after the minister had finished a bruising session giving evidence at the Leveson Inquiry into press ethics and standards last Thursday (May 31).
Cameron also said that he would not refer Hunt to the independent adviser on the ministerial code, Sir Alex Allan.
Hunt took on the role of adjudicating on the Sky bid in December 2010 after business secretary Vince Cable said that he had "declared war" on News Corp boss Rupert Murdoch.
Prior to that, Hunt had publicly expressed his support for the bid.
But appearing on BBC One's Andrew Marr show on Sunday, June 3, the Prime Minister insisted that Hunt had always acted on the legal advice he had received.
Cameron said that the Culture Secretary had given "a good account of himself" to the Leveson Inquiry and to parliament.
"The advice I was given was that what mattered was not what Jeremy Hunt had said publicly or privately but how he was going to conduct himself during the bid," he said.
"That's how I think we should judge him: did he adjudicate this bid wisely and fairly?
"And he did. He took legal advice at every stage, and he followed that legal advice and he did many things that were not in the interests of the Murdochs or BSkyB and that side of things."
"I took the advice of the Cabinet Secretary, who took legal advice about it, and what he (Hunt) said publicly was more effusive, more powerful than anything he'd said privately, and on that basis I gave him the job," said Cameron.
The Prime Minister declared that Hunt had "given a good account of himself to the Leveson Inquiry, he's given a good account of himself to parliament, and I think that's the key point".
He added that Hunt "ran the bid very well and, I think, reached the right conclusions".
However, Labour has said that it intends to use the next scheduled day of debate in the Commons, June 13, to ask MPs to vote on whether the Culture Secretary should be investigated.
The Liberal Democrat leader Nick Clegg is expected to give evidence to the Leveson Inquiry on that day, followed by the Prime Minister the day after.