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BBC business editor Robert Peston says Mr Agius will admit to an "unacceptable standard of behaviour" at Barclays when he makes the announcement on Monday.
It comes after Barclays was fined £290m ($450m) for attempting to manipulate the Libor inter-bank lending rate.
Earlier, it emerged RBS had sacked four traders over their alleged involvement in the Libor-fixing scandal.
The dismissals happened at the end of last year.
Our correspondent says Mr Agius made his decision to quit on Saturday night.
In his resignation statement he is expected to say the scandal had been a "devastating blow to the bank's reputation" and apologise to staff, customers and shareholders.
MPs' questions
Barclays was fined after the Financial Services Authority (FSA) found its traders had lied about the interest rate other banks were charging it for loans. Investigations are also under way at RBS, HSBC, Citigroup and UBS.
There is a perception, which is perhaps false, that he is not quite tough enough" Giving a lower reading than the true rate would give the impression other banks thought it was a better risk to lend to than it was.
Libor (London Inter Bank Offered Rate) is the rate at which banks in London lend money to each other.
Our correspondent said Sir John Sunderland will the lead search for a new chairman and Mr Agius will remain in post pending that appointment.
The early favourite to succeed Mr Agius is Sir Mike Rake, BT chairman and senior independent director at Barclays.
Our correspondent said some shareholders did not think Mr Agius, who had been chairman for six years, was tough enough to stand up to Barclays chief executive Bob Diamond, who was regarded as very talented but also very headstrong.
Mr Diamond has insisted he will not resign over the scandal.
He is due to appear before the Commons Treasury Select Committee on Wednesday, with Mr Agius set to follow on Thursday.
The BBC's business editor said earlier that, in making false submissions about their borrowing costs, Barclays managers believed they were operating under an instruction from Bank of England deputy governor Paul Tucker.
He said this belief came about after a telephone conversation in the autumn of 2008 between Mr Tucker and Mr Diamond, who at the time ran Barclays' investment bank, Barclays Capital.
Mr Tucker did not issue this instruction. But he and Mr Diamond have different recollections of their conversation.
So what Mr Diamond recalls about this telephone conversation might turn out to be the most explosive and important part of his testimony to MPs on the Treasury Select Committee, our correspondent added.
Independent review
In a letter to the committee last week, Mr Diamond condemned the inappropriate behaviour of a "small number" of employees who had tried to make profits for their own benefit.
In his open letter to chairman Andrew Tyrie MP, Mr Diamond pointed out that authorities found no evidence that knowledge of the manipulation, for which it has been fined £290m, went any higher than "immediate desk supervisors".
Robert Peston said he believed Barclays board had "thrown its weight" behind Mr Diamond, considering him to be the best man to clean up the bank's culture.
Earlier, the head of the Financial Services Authority, Lord Turner, said the FSA's fine for Barclays was its strongest currently available sanction and the law should be tightened to tackle misbehaviour in banking.
He told the BBC's Andrew Marr programme there should be a presumption a director of a failed bank should not work in the industry again.
Business Secretary Vince Cable is considering criminal sanctions for bank directors. He said those in charge of failed banks should face prosecution - a view echoed by Lord Turner.
Ministers have announced an independent review of the Libor workings, which will be established next week and report by the end of summer.
On Saturday, Labour leader Ed Miliband called for a public inquiry into the customs and practices of the banking industry.
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