"This is both a good and a practical solution," Finance Minister Eveline Widmer-Schlumpf told reporters on Wednesday after a cabinet meeting approved the draft accord.
She declined to give details of the sum that the banks will have to pay US revenue authorities in order to win legal closure, though Swiss media have reported that the overall figure could hit 10 billion francs ($10.3 billion).
"If a bank has done a lot of business involving undeclared American funds, it will be a big problem for it," Widmer-Schlumpf said.
She indicated that the Swiss government had been presented with a take it or leave it offer by Washington.
"It was a unilateral offer, one that we couldn't negotiate," she said.
She rejected reports that the Swiss taxpayer would have to come up with at least part of the funds.
"Switzerland will pay nothing," she insisted.
The deal, which will require approval by parliament, frees up Swiss banks to circumvent some elements of secrecy laws and turn over key information to US authorities.
Washington has repeatedly accused Swiss banks of complicity in tax evasion, since they hold billions of dollars belonging to American citizens accused of hiding away taxable income from the US revenue service.
"We hope that it will enable this chapter to be closed," Widmer-Schlumpf said, noting that it was nonetheless up to individual banks to decide if they wanted to cooperate with US authorities.
However, any bank failing to toe the line risks being barred from the US market.
Widmer-Schlumpf underlined that the goal of the deal was to create a legal framework under which the banks themselves could win legal closure of their disputes with the United States.
A bill on the deal will be put to parliament next month, and the implementation of its provisions will be limited to one year.
In a statement, the government said the bill "authorizes banks to cooperate with the US authorities and to make available the information necessary to safeguard their interests".
"This includes in particular information about business relationships concerning US persons and details on people who were involved in the US business of the respective banks," it said.
With the global economic crisis having put tax havens into sharp focus, Switzerland has fought to defend its long-cherished principle of banking secrecy by giving ground in some areas but declining to allow the automatic handover of account details.
The government said that while the names of US clients can be handed over automatically, their account details can only be disclosed if Washington makes a specific request under rules related to the pursuit of tax dodgers.
Previous reports have said the 300 banks in Switzerland would be ranked by their level of alleged complicity in tax evasion.
The dozen seen as the main offenders would reportedly be forced to make individual deals, while a second category, comprising those with American clients but which have not yet faced legal action in the United States, would have to pay a set fine.
Under the accord agreed , Swiss banks will give details of employees who deal with American clients.
In April 2012, Washington won the handover of the names of 10,000 such employees from some Swiss banks.
That came after a green light from the government, which faced criticism from banking sector employees for potentially exposing them to charges of abetting tax evasion.
The new deal would be far larger in scope, and the government said banks "will be obliged by law to provide maximum protection for their employees", including against dismissal, with a 2.5-million-Swiss-franc fund created by the banks for this purpose.