The bank violated federal tax laws, and helped people to open forged accounts in Hong Kong, Panama and Liechtenstein, the US Department of Justice said.
The penalty came after the bank accepted in January this year that it failed to implement necessary measures to stop tax evasion by its US customers.
The plea agreement comprises a $22m criminal fine, forfeiture of $15.8m and a payment of $20m, representing the amount of taxes avoided by its US account holders.
Additionally, the lender also agreed to surrender $16.2m to the government, amounting to a total recovery of approximately $74m.
Manhattan US Attorney Preet Bharara said, "Wegelin has now paid a steep price for aiding and abetting tax fraud that should be heeded by other banks, bankers, and advisers who engage in the same conduct."
"U.S. taxpayers with undeclared accounts – wherever those accounts may be – should know that their bank may be next, and they should pay what they owe the IRS before we come find them."
Wegelin, which was set up in 1741, has no other branch outside Switzerland and is planning to wind down its operations in the US, following the settlement of its legal case.