Mr Agius, 64, will step down after Barclays was fined a record £290 million by the Financial Services Authority (FSA) over the practice last week.
The regulator found the firm's traders had lied about the interest rate other banks were charging it for loans.
News of Mr Agius's imminent departure leaked last night, after it emerged that Royal Bank of Scotland had sacked four of its staff for alleged involvement in rigging the Libor inter-bank lending rate.
The part-taxpayer-owned Edinburgh institution is already under investigation over the allegations, along with HSBC, Citigroup and UBS.
Traders Paul White and Neil Danziger, investment adviser Andrew Hamilton and Tan Chi Min, formerly with RBS in Singapore, were sacked between the end of last year and February amid claims of rate rigging.
Mr Agius will depart three days before he is due to be quizzed by MPs on the House of Commons Treasury Committee.
It will put more pressure on Barclays chief executive Bob Diamond, who is resisting calls for his own resignation and is due to appear before the Treasury Select Committee on Wednesday.
Last night a spokesman said Mr Agius was still expected to attend.
As the outcry over the scandal intensified, senior figures lined up yesterday to call for a police investigation.
FSA head Lord Adair Turner called for a change in the law if necessary to prosecute those guilty of interest-rate fixing.
There are also increasing demands for the senior executives of banks to explain what they knew and when about the scandal.
As part of an effort to clean up the banking industry, ministers will tomorrow unveil proposals designed to crack down on a culture of bad behaviour in the City.
Under the plans, senior executives in charge of banks that fail could be banned from heading similar organisations again. Directors could also be forced to give up much of their salary if the banks they run collapse.
Ministers are keen to be seen to be clamping down on the behaviour of bankers following a torrid week of scandals.
A day after the Barclays fine was announced, four of the UK's largest banks, including RBS, admitted mis-selling complex financial instruments to small businesses, a practice that forced some to go bust.
At the weekend, opinion polls showed the vast majority of those questioned wanted corrupt bankers to be prosecuted.
But Which? also found two-thirds of people did not trust the Government to act in their best interests when regulating banks.
Lord Turner told the BBC's Andrew Marr programme he had recommended ministers bar bosses of failed banks from working in the industry again, following a review of the billion-pound taxpayer bailout of RBS under the previous Labour government in 2008.
Ministers are keen to ensure no repeat of the outcry that surrounded revelations about former RBS chief executive Fred Goodwin's lucrative pension package following the bailout.
While the proposals will go some way to assuaging public fears over the state of the banks, the Coalition remains under intense pressure to order a judge-led investigation into the rate-rigging scandal. Ministers have already announced plans for a review,
which they say should be swift enough to allow for potential changes to the Financial Services Bill currently going through the Westminster parliament.
Shadow Business Secretary Chuka Umunna said that a review would not get to the heart of the problems that allowed the manipulation of the Libor rate, which governs lending between banks.
"This isn't just a few rogue traders or bad apples, this is something that is cultural," he said. "And that's why we're calling for a commission to look into this. The industry, the banking sector, have got to wake up and smell the coffee."
Stewart Hosie, SNP Treasury spokesman, called for "full transparency", saying both Labour and the FSA had questions to answer about what happened on their watch.
Last night it was reported that Mr Diamond had met staff at investment bank Morgan Stanley and suggested he was relatively upbeat about the longer term – but said things would get worse before they got better. A newspaper reported the contents of a memo from analysts at Morgan Stanley that said Mr Diamond feared the scandal would lead to "more political intervention" and reinforce the "bad caricature" of the industry.
Sir Mike Rake, the chairman of BT, is tipped to replace Mr Agius.