Giving evidence to the Treasury Select Committee (TSC), Marcus Agius said the non-executive board members hoped to keep Mr Diamond as CEO but the regulator "lost trust" in the bank's boss.
He revealed that Bank of England governor Sir Mervyn King prompted the resignation of Mr Diamond early last week.
He said that King called senior directors of Barclays to a meeting and made it clear that Britain's financial regulators no longer supported Mr Diamond's ongoing position.
Mr Agius also revealed that the public anger over the scandal was far larger than senior executives had predicted.
Talking about Mr Diamond's decision to resign, Mr Agius said he "was not in a good place" and "asked for time to talk to his family".
"I left his house confident he would resign. As you can imagine it was a busy night," Mr Agius, who first employed Mr Diamond, said.
Mr Diamond waived a bonus worth up to £20m, Mr Agius told members of the committee.
He added that Mr Diamond left the company with his annual salary and pension entitlements valued at some £2m.
"He will get 12 months' pay and a cash payment in lieu of pension of around £2m," Mr Agius said.
Mr Agius later revealed that Mr Diamond had a six-month notice period but would be given 12 months' notice to "maintain goodwill".
Asked by one MP if that means Mr Diamond is on "gardening leave", Mr Agius said: "If that is what you want to call it."
He said that it was important to keep a good relationship with the ex-CEO as he would consider calling on Mr Diamond to help Barclays in the future.
The official spokesman for Prime Minister David Cameron commented on the decision by Mr Diamond to waive his bonus.
The spokesman said: "I think the decision to forgo the bonus is a sign that they understand public concerns and that they understand that there is a need for a change in the culture of banks."
Mr Agius said he was "truly sorry" about the Libor rate-fixing scandal that has tarnished his bank but refused to comment on if manipulation was more widespread in the industry.
The rate-fixing took place in Barclays Capital at a time when Mr Diamond headed the investment arm, however giving evidence last Thursday Mr Diamond said he had only been told about rate manipulation last month.
Mr Agius admitted that as chairman he first hearing about the topic in April, 2010.
Asked why Mr Diamond gave conflicting evidence to the TSC about a letter sent by the Financial Service Authority to the bank, Mr Agius said: "I can't comment on Mr Diamond.
"I am not going to speak to Mr Diamond's testimony."
He told MPs that the economic crisis at his bank several years ago put it in a state of "existential risk" when the scandal occurred.
"It doesn't mean it was right... but it shows the extraordinary situation at the time."
When asked about being chairman of a bank that paid three times the amount as bonuses to bankers than it did to shareholders - including pensioners - Mr Agius said it was "simplistic" to pay staff less.
"Barclays has been around for 300 years and I would like to think it will be around for another 300 years," Mr Agius added.
"The culture at Barclays is honest, customer-centric and competitive."