MIAMI/ZURICH (Reuters) - The days of secret bank accounts are numbered for Americans after UBS and the US and Swiss governments agreed to settle a dispute over whether the Swiss bank should be forced to disclose the names of 52,000 rich US clients suspected of tax evasion.

Lawyers involved in the case said yesterday's settlement could involve the disclosure to US authorities of 3,000 to perhaps more than 10,000 names of American clients suspected of using offshore accounts to evade taxes.

While details weren't disclosed, the parties have initialed agreements that will "take a little time to be signed in final form", Department of Justice lawyer Stuart Gibson told US District Court Judge Alan Gold during a brief conference call.

The case is expected to be dismissed once a final agreement is in place. UBS and the government had reached a settlement in principle on July 31.

The deal is also expected to put European tax dodgers on notice as other governments are encouraged to seek out hidden accounts. US authorities believe the 52,000 US-based clients of UBS may be hiding nearly $15 billion of assets.

Alfred Mettler, a Georgia State University finance professor and member of a Swiss task force on bank secrecy, said it would likely take months to implement the UBS pact, and may foreshadow an IRS push to ferret out suspected tax cheats.

"The IRS will certainly increase its efforts to go after non-taxed money wherever it is," he said. "But you need some evidence, and my guess is other banks, not only Swiss banks, must have taken steps to be proactive."

Washington's case against UBS, the world's second-largest wealth manager, had strained relations between the US and Switzerland because it challenged the latter's jealously guarded bank secrecy laws.

UBS shares closed three percent higher in Switzerland and were up more than four percent in afternoon trading in New York.

"This is definitely good news for UBS," said Milan Patel, a tax lawyer at Withers LLP in Geneva.

"However, this may mean that UBS could face a new legal battle in Switzerland if the account holders claim UBS violated Swiss bank secrecy laws by disclosing their names," Patel added. "Thus, UBS may have ended the US legal battle only to start the Swiss legal battle."

In February, UBS agreed to pay $780 million to settle criminal charges in a similar dispute with the US government. The bank agreed to hand over data on about 250 US clients, and promised to close its offshore business to US clients.

UBS Chairman Kaspar Villiger said the bank was "grateful" that the two governments had resolved their differences in the latest case. The bank said it expected a final agreement "in the near future".

Doug Shulman, commissioner of the Internal Revenue Service, the US tax collection agency, said the pact with Switzerland "protects the United States government's interests".

Both governments must now sign off on the settlement, the Swiss Justice Ministry said.