Sir James said in his statement that HBOS had "extensively investigated" Mr Moore's allegations, concluding that they "had no merit". Mr Moore was the former head of risk at HBOS.
"I nonetheless feel that the right course of action for the FSA is for me to resign from the FSA board, which I do with immediate effect," Sir James added.
The FSA said: "[The] specific allegations made by Paul Moore in December 2004 regarding the regulatory risk function at HBOS were fully investigated by KPMG and the FSA, which concluded that the changes made by HBOS were appropriate."
"It should also be noted that the FSA's concerns about HBOS' risk management framework considerably pre-dated the allegations by Mr Moore," the FSA said in a statement.
It said that it conducted a full risk assessment of HBOS at the end 2002, "which identified a need to strengthen the control infrastructure within the group".
A risk assessment of the HBOS group, formally recorded in December 2004, showed that "the group had made good progress in addressing the risks highlighted in February 2004, but that the group risk functions still needed to enhance their ability to influence the business, which we saw as a key challenge", the FSA said.
It said it had "continued to pursue concerns about the risk management framework" and wrote to HBOS on 29 June 2006, stating that "whilst the group had made progress, there were still control issues" and that "the growth strategy of the group posed risks to the whole group and that these risks must be managed and mitigated".
Whistleblower on Crosby resignation
Mr Moore had earlier released a statement in reaction to Sir James' resignation.
He said: "I read with interest that Sir James continues to refute the allegations I made in my evidence to the Treasury Select Committee and I want all those interested to know that I continue to stand firmly and confidently behind what I have said."
He was not interested in blame and had received countless messages of support, he added.
The Treasury, for which Sir James had worked as an adviser, said officials had been in contact with the City watchdog, but pointed out that ministers had had no direct contact with either Sir James or the FSA in the last 24 hours.
SIR JAMES CROSBY
Born 1956. Educated at Brasenose College, Oxford
Joined the Halifax in 1994 and became chief executive in 1999
Became chief executive of HBOS in 2001 following the merger of the Halifax with the Bank of Scotland
Left HBOS in 2006
Appointed to the board of the Financial Services Authority in 2004, and became deputy chairman in December 2007
Led two inquiries for the Treasury: The first in 2006 on identity fraud, the second in 2008 on the mortgage market
The Treasury told the BBC it was Sir James' personal decision to resign from the FSA.
Speaking in Prime Minister's Questions, Gordon Brown said it was right that Sir James stepped down from the FSA.
"It is right that we investigated serious allegations that are made about the banking system. These are serious but contested allegations," he said.
The episode has given the Prime Minister's enemies their first chance to link Gordon Brown personally with someone who, it is alleged, ignored warnings that brought down the Halifax, says the BBC's political editor Nick Robinson.
Opposition leader David Cameron accused the Prime Minister of a "serious error of judgment" in appointing Sir James to the FSA.
David Cameron: Gordon Brown should admit he's made a mistake
Michael Fallon, a Conservative MP on the Treasury Committee, said there were questions not only over the dismissal of Paul Moore from HBOS but over how the bank got into financial trouble.
Under Sir James, HBOS had made "mistakes other banks didn't make", he said.
The Treasury Committee had received written evidence from Mr Moore on Tuesday.
Mr Moore claimed he was "summarily dismissed" as the head of group regulatory risk at HBOS by Sir James.
"He [Sir James] said I had lost the confidence of key executives and non-executives, but refused to explain why," said Mr Moore in a recent written submission to the Treasury Committee.
The bank says Mr Moore was made redundant following a restructuring and was replaced by a banker with 20 years' experience, who reported directly to the chief executive.
Mr Moore told the BBC earlier this week that he saw evidence of "negligence" and even "recklessness" during his time at the bank.
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