Former director-general George Entwistle will receive one year's salary after resigning from the BBC.
Mr Entwistle quit after 54 days in the job after a Newsnight report wrongly implicated former Conservative Party treasurer Lord McAlpine in an investigation into child abuse allegations at the Bryn Estyn care home in North Wales.
Under the standard executive board contract, he would normally be entitled to just six months salary.
A BBC Trust spokesman said: "The BBC reached a consensual termination agreement with George Entwistle last night and agreed to pay him 12 months pay, in lieu of notice.
"This reflects the fact that he will continue to help on BBC business, most specifically the two ongoing inquiries."
The chairman of the Commons Culture, Media and Sport Committee John Whittingdale said he could not see any justification for such a large payoff.
"A lot of people will be very surprised that somebody who was in the job for such a short period of time and then had to leave in these circumstances should be walking away with £450,000 of licence fee payers' money," he said.
"Certainly I would want to know from the Trust why they think that's appropriate.
"I want to hear an explanation but I have to say that I find it very difficult to see a justification for that amount of money to be paid to somebody who has had to resign in these circumstances.
"I wouldn't have thought that just because you have to help an inquiry into the Savile allegations you necessarily need to be paid a such a large amount of money.
"A lot of people will be giving evidence to the inquiry into the culture and practices within the BBC and I can't imagine they will all be being paid for it."
The chairman of the BBC Trust, Lord Patten, has told Sky News that people will expect him to step down if he fails to restore the public's confidence in the corporation.
"If we don't restore the huge confidence and trust that people have in the BBC, then I'm sure people will tell me to take my cards and clear off," he said.
He also admitted that the future of Newsnight is being discussed.
Tim Davie, the acting director-general of the BBC, will unveil his plans to restore the broadcaster's reputation on Monday.