The bank said it would “cease to operate” yesterday after it agreed in a New York court to pay US authorities $57.8m (£35.9m) in compensation and fines.
Wegelin & co, established in 1741, admitted to helping over 100 US taxpayers hide approximately $1.2bn (£747m) for almost ten years.
It is the first institution to plead guilty to tax evasion charges in the US and the case could prove an important moment in a US focus on Swiss banking secrecy.
In recent years other Swiss banks moved to prevent US citizens from opening offshore accounts.
US Attorney Preet Bharara said it is 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."
"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."
Otto Bruderer, managing partner at Wegelin, told the court the bank “was aware that this conduct was wrong."
He added 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 Internal Revenue Service".
The US crackdown took shape from 2009 when UBS, Switzerland’s biggest bank, agreed to turn over 4,450 client names and pay a fine of $780m in a plea deal as part of a wide-ranging tax-evasion case.
Switzerland's other major bank, Credit Suisse is also under investigation by the US authorities, as is high profile bank Julius Baer and 11 other mainly local banks.