Paul Revere never yelled “The British are coming” on his famous midnight ride in 1775—he shouted, “The Regulars are out,” using a common term for British soldiers.

But if the silversmith were alive today, he would be justified in galloping through the countryside to warn the nation's richest citizens: The Swiss are coming—and they want you and your money.

Swiss wealth managers largely pulled out of the U.S. market in recent years after UBS was accused of helping clients hide offshore accounts from the Internal Revenue Service. However, some are coming back across the pond because they see enormous growth potential, according to a report issued last month by Boston-based research and advisory firm Aite Group. The report said Swiss managers could target $100 billion in North American assets—seven times what they currently manage.

The exodus began after UBS, the largest Swiss bank, agreed to pay $780 million in fines in 2009 and turn over information on more than 4,000 secret accounts to settle charges it helped clients conceal assets from the IRS. Just last month, fugitive banker Raoul Weil, former head of the wealth-management division of UBS, was arrested in Italy to face U.S. charges relating to his alleged role in the scheme.

Wegelin & Co., Switzerland’s oldest private bank, was another casualty that closed its doors after pleading guilty to abetting income tax evasion.

The U.S. is the world’s leading wealth management market. So, a growing number of advisors have refocused on the U.S. market in anticipation of a landmark agreement reached by U.S. and Swiss authorities in September, the report said. The agreement allows mostly smaller Swiss banks—those not currently under investigation—to disclose hidden U.S. assets and avoid prosecution.

As of March, the number of Swiss-based RIAs jumped to 51, up from 10 in 2007, according to the Aite report, which tracked the number of firms filing as advisors with the Securities and Exchange Commission. The number of Swiss firms engaged in wealth management jumped eightfold, according to the report, Offshore U.S. Private Wealth: Switzerland’s Compliant Re-Engagement.

“The natural conclusion is that the rise is a direct result of the U.S. authorities dictating a new model of compliance,” the report said, adding that some Swiss firms consider the U.S. “a strategically important market for their business, either due to an existing client base or the potential to develop one.”   

Switzerland is still the world’s largest private offshore wealth center and will benefit from clients seeking geographic diversification, the report said. Switzerland attracts $2.2 trillion, or about 26 percent of the world’s total offshore assets of $8.5 trillion, according to Boston Consulting Group. It is nearly double the size of the No. 2 region: Singapore and Hong Kong.

However, it holds less than 6 percent of the $780 billion in North American offshore assets, most of which are in the Caribbean, Panama, the United Kingdom and the Channel Islands.