This investigation will take place under section 77 of the Financial Services Act 2012, says the FCA.
The FCA says it fully agrees that the investigation should be led by an independent person and says it looks forward to supporting them in their work. The FCA says it will make its full resources available to support the investigation.
The watchdog says it is important that the timing of the investigation must not prejudice any other criminal or regulatory proceedings. The FCA is already undertaking work to establish whether it should commence a formal enforcement investigation and expects to reach a conclusion shortly.
Chancellor George Osborne was announcing the inquiry details this afternoon.
Concerns have been raised in several quarters about the running of the bank. Former chairman Paul Flowers has been held by Merseyside police in relation to a drugs supply investigation.
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The Treasury has jointly agreed the independent inquiry with the Prudential Regulation Authority (PRA) and the Financial Conduct Authority (FCA). It has not yet been announced who will lead the inquiry which may be separate from any regulatory investigations.
The independent investigation under the Financial Services Act will therefore not start until it is clear it will not prejudice any actions the relevant authorities may take, including the potential FCA and PRA enforcement investigations.
The Treasury says that the detailed direction that will order the independent investigation and set out its terms will take into account any issues arising, including from the potential FCA and PRA enforcement investigations and be determined in consultation with the independent person appointed to lead it.
A Treasury spokesman said: "It will cover the actions of relevant authorities (regulators and government) and the institution itself, including prudential issues, governance (including the appointment of senior staff) and acquisitions. The period that the investigation will review will start from at least 2008 and run to at least the present time. The direction and the investigation's report will be laid before Parliament.
"The government is determined to create a stronger and safer banking system. A key part of this is reforming the regulatory regime for senior managers. That is why the government's Banking Reform Bill, which is currently passing through the House of Lords, will introduce a new senior managers' regime, subjecting decision makers in banks to higher standards that means if they fail in their duties they will be held to account."