Switzerland's oldest bank is to close permanently after pleading guilty in a New York court to helping Americans evade their taxes.
Wegelin, which was established in 1741, has also agreed to pay $57.8m (£36m; 44m euros) in fines to US authorities.
It said that once this was completed, it "will cease to operate as a bank".
The bank had admitted to allowing more than 100 American citizens to hide $1.2bn from the Internal Revenue Service for almost 10 years.
Wegelin, based in the small Swiss town of St Gallen, started in business 35 years before the US declaration of independence.
It becomes the first foreign bank to plead guilty to tax evasion charges in the US.
Other Swiss banks have in recent years moved to prevent US citizens from opening offshore accounts.
US Attorney Preet Bharara said: "The bank wilfully and aggressively jumped in to fill a void that was left when other Swiss banks abandoned the practice due to pressure from US law enforcement."
He added that it was a "watershed moment in our efforts to hold to account both the individuals and the banks - wherever they may be in the world - who are engaging in unlawful conduct that deprives the US Treasury of billions of dollars of tax revenue".
Otto Bruderer, a managing partner at the bank, admitted that Wegelin had sheltered US clients from tax between 2002 and 2010, and said it was aware that its conduct had been "wrong".
Mr Burderer's further admission that assisting tax evasion was common practice in Switzerland has caused huge concern among the Swiss banking community, according to the BBC's Switzerland correspondent, Imogen Foulkes.
"Some Swiss financial analysts are already speculating that Wegelin's $58m fine, which many had expected to be higher, was kept low by the US authorities in return for Wegelin clearly implicating the rest of the Swiss banking community in tax evasion," she said.
Wegelin effectively ceased to function as a Swiss bank almost a year ago.
US criminal accusations against three of its executives prompted the bank to sell off its core Swiss and other non-US businesses in January 2011.
The rushed sale protected Wegelin's non-US clients from the fall-out of any legal battle, and reflected fears that few clients would want to continue doing business with a bank being pursued by the US anyway.
The businesses were bought by Raiffeisen Bank, Switzerland's co-operative bank, which has since severed the few business ties that it had with the US.
The sale left Wegelin responsible only for its American clients, including those at the centre of the US authorities' probe.
Wegelin as an institution was then itself indicted by US authorities in February last year, and later declared a fugitive from justice when the bank's executives failed to appear in a US court.
The bank had vowed to fight the charges, claiming that because it only had branches in Switzerland, it was bound only by its home country's relaxed banking laws.
Its decision to cave in, and wind down its one remaining business, has made the bank's demise inevitable.
"Usually when you cave in to the USA, you do it because you just want to get rid of it," said Dr Peter V Kunz, an economic law professor at the University of Bern.
Having sold off all its non-US businesses, Mr Kunz believes the bank's partners would have been keen to end a potentially interminable legal dispute with the US in order to recover as much of the sale proceeds as possible from what had in effect become a shell company.
The desire to end the legal battle would have been given added pique by the fact that Wegelin's partners have personal financial liability for the bank.
Jeffrey Neiman, a former US federal prosecutor who was involved in a previous investigation into Swiss banks, said: "It is unclear whether the bank was required to turn over American client names who held secret Swiss bank accounts.
"What is clear is that the Justice Department is aggressively pursuing foreign banks who have helped Americans commit overseas tax evasion."
It remains to be seen whether US authorities will continue with, or drop, parallel charges against three Wegelin bankers, Michael Berlinka, Urs Frei and Roger Keller.
The decision to throw in the towel also marks a turnaround for Konrad Hummler, Wegelin's managing director since 1991, and one of the partners whose own personal finances were potentially at stake.
Mr Hummler, who is also chairman of the Swiss daily newspaper Neuer Zuercher Zeitung, has previously been unusually outspoken among Swiss bankers in calling for the country's authorities to block any disclosure of banking client details to the US authorities.
The Wegelin case comes four years after a far larger Swiss bank, UBS, agreed to pay a $780m fine to US authorities related to tax evasion charges. UBS also agreed to reveal the details of US account holders.
However, UBS neither pleaded nor was found guilty. Instead it and US prosecutors came to what is called a deferred prosecution agreement, with the fine being paid in exchange for the charges being dropped.
Switzerland's other major bank, Credit Suisse - with over a trillion dollars in total assets and another trillion in clients' money - remains under investigation by the US authorities, as does another high profile bank, Julius Baer, which is about a fifth of the size of Credit Suisse, as well as 11 other mainly local, cantonal banks.