The plea, entered in the US District Court in Manhattan is the final chapter in the history of a bank which dates back to 1741, although a question remains as to whether the firm has handed over, or will disclose, names of US clients to the US authorities.

An end to such a bank - the oldest in Switzerland - has been seen as a sign of how large countries such as the US are determined to hunt alleged tax evaders using Swiss and other countries' offshore accounts. In 2009, Switzerland's biggest bank, UBS, paid $780 million to settle civil charges of aiding US tax evaders and also settled criminal charges over such matters. Just as significantly, UBS agreed that some client data should be handed to the US authorities, seen as a major breach of Switzerland's centuries-old tradition of banking secrecy.

Wegelin, located in the small Swiss town of St Gallen, admitted to charges of conspiracy in helping US clients evade taxes on at least $1.2 billion. Wegelin agreed to pay $57.8 million to the US in restitution and fines.

Otto Bruderer, a managing partner at the bank, said in court that "Wegelin was aware that this conduct was wrong”, according to a report by Reuters.

He reportedly said that "from about 2002 through about 2010, Wegelin agreed with certain US taxpayers to evade the US tax obligations of these US taxpayer clients, who filed false tax returns with the IRS."

Wegelin vowed to contest the charges when it became the first foreign bank in recent times to be indicted by the US authorities. Yesterday’s announcement means Wegelin’s name will entirely vanish from the banking world.

"Once the matter is finally concluded, Wegelin will cease to operate as a bank," Wegelin said in a statement emailed to this publication.

News reports said the fate of three Wegelin bankers, indicted in January 2012 on charges later modified to include the bank, remains unclear. Under criminal procedural rules, the cases of the three bankers - Michael Berlinka, Urs Frei and Roger Keller - are still pending.

A year ago, Wegelin & Co Private Bankers transferred a substantial majority of clients and staff to Notenstein Private Bank, which became a 100 per cent subsidiary of Raiffeisen Switzerland.

The Wegelin statement said: "Under the terms of the plea agreement, Wegelin admitted that between 2002 and 2010 it violated US law by opening and maintaining bank accounts for US taxpayers. For its role in the offense, the plea agreement calls for Wegelin to pay a sum of approximately $57.8 million that is comprised of restitution for lost taxes , forfeiture of gross revenues attributable to the bank’s business with US clients , and a fine . It also requires Wegelin to ensure the safe-keeping of US client data pending further instruction from competent Swiss authorities."

The bank said it co-operated with investigators since learning it was being probed by US authorities.

"As a practical matter, today’s plea brings to an end the criminal prosecution of Wegelin conducted by the US Attorney’s Office for the Southern District of New York and the Internal Revenue Service. A judgment of conviction marking the formal end of the matter will issue after the Court imposes sentence. The monies required to be paid in connection with the Bank’s sentencing  will be paid from funds specifically set aside to cover legal risks. Once the matter is finally concluded, Wegelin will cease to operate as a bank," the firm said.

Wegelin & Co has said that it will not be commenting further with regards to the settlement agreement.