The deals are another step in Swiss efforts to clean up the country’s image, under pressure from American prosecutors as well as European countries that have been willing to pay for lists of client names that were stolen by bank employees.

“Being surrounded by the E.U. and a significant wealth management center, Switzerland has chosen to make this move earlier rather than later,” said Luc Thévenoz, a law professor at the University of Geneva.

The treaty with Germany is likely to be signed first, possibly as early as Wednesday, followed by a similar deal with Britain.

Both agreements should have broad effects, analysts and lawyers say. Clients will be able to retain secrecy, but at a price, and some may choose to move to other offshore locales.

Britain and Germany will win billions in needed revenue and, in return, will no longer pursue Swiss banks in criminal cases related to a lack of compliance with tax rules. And the Swiss banking model will shift further from reliance on managing undeclared money. That will particularly affect smaller banks.

Banking secrecy was enshrined in law in Switzerland in the 1930s and has been used to protect anonymity as well as to evade taxes, which is not in itself a crime under Swiss law. But under increasing international pressure, Switzerland agreed in 2009 to apply new standards in bilateral tax treaties, allowing for an exchange of information in tax evasion as well as fraud cases. It has since incorporated those rules into some 30 bilateral double-taxation agreements.

“The whole structure of Swiss banking secrecy has already changed,” said Pietro Sansonetti, a partner at the Geneva offices of the law firm Schellenberg Wittmer. “Secrecy can still protect privacy for personal reasons but no longer for simple tax avoidance.”

The new treaties will be much more sophisticated and broader than existing accords with the European Union, in force since 2005, which charge a withholding tax on interest income on savings. That levy is then returned anonymously to the home country, but it is easy for depositors to mask their identities.

After the deals are ratified by legislatures, German and British clients would pay a one-time retroactive sum on their capital, as well as an annual tax on capital gains and dividend payments rather than just on interest income.

Germany and Britain will consider the withholding tax as final and their citizens will no longer have the legal obligation to declare their Swiss income to their home authorities.

Mario Tuor, a Swiss government spokesman for finance, said negotiations with Germany were in their “final phase” and talks with Britain were moving “in a parallel track.” He declined to provide further details.

A German official, who was not permitted to speak publicly, said an agreement was “very close.” The British Revenue and Customs department said “constructive discussions are continuing with the Swiss authorities, and we hope to conclude these as soon as possible.”

The Swiss newspaper SonntagsZeitung reported last weekend that a deal with Germany could be announced Wednesday, and would include a one-time payment of 2 billion Swiss francs, or $2.7 billion, to cover the last 10 years, and a future withholding tax of 26 percent. Swiss banks would make the initial payment and then recoup it from their German clients.

The figures could be higher in the deal with Britain, where similar income would be taxed at progressive and probably higher rates.

If successful, the agreements might then be replicated by other European countries like France, Italy and even struggling Greece.

Washington has followed a different path. American clients are obliged to inform United States tax collectors of their Swiss assets. And the authorities have been conducting investigations involving Americans with undeclared funds in Switzerland since a landmark case in 2009 against UBS. The Swiss bank was forced to identify some of its American clients and was fined $780 million for helping tax evasion. The Swiss government agreed that further client names could be provided if it were shown that other banks acted like UBS.

This article has been revised to reflect the following correction:

Correction: August 10, 2011

An earlier version of this article paraphrased incorrectly an assessment by Louise Somerset, tax director at RBC International Wealth Planning in Britain. She said the agreements might put the onus on Singapore and Hong Kong to enact similar deals to clamp down on tax evasion, not tax avoidance.

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