He will remain in his post until an orderly succession is assured. Sir Michael Rake, BT chairman and senior independent director at Barclays, has been appointed deputy chairman, the BBC has reported.
Meanwhile, Sir John Sunderland, a non-executive director of Barclays, will begin the search for a new chairman.
In his resignation letter, Agius said: “It has been my privilege to serve as Barclays chairman for the past six years.
“This has been a period of unprecedented stress and turmoil for the banking industry in particular and for the wider world economy in general.
“But last week’s events- evidencing as they do unacceptable standards of behaviour within the bank have dealt a devastating blow to Barclays reputation.
“As chairman I am the ultimate guardian of the bank’s reputation. Accordingly the buck stops with me and I must acknowledge responsibility by standing aside.”
Agius’ resignation comes after Barclays was fined £290m ($450m) for attempting to manipulate the Libor inter-bank lending rate. He is due to appear before the Treasury Select Committee to answer questions on the issue on Thursday.
Barclays’ chief executive Bob Diamond will appear before the Committee the day before. Analysts do not expect him to follow Agius’ lead and resign from the bank.
Investigations are also under way at RBS, HSBC, Citigroup and UBS over the Libor rate fixing scandal.