(Corrects description of J. Safra Sarasin in first paragraph to Swiss private bank, from Brazilian-Swiss)
* Price for Morgan Stanley Swiss unit not disclosed
* J. Safra Sarasin acquiring 10 bln Sfr in assets - source
* Swiss Morgan Stanley unit has opted for U.S. tax programme
* Deal to close by end June 2015
ZURICH, April 30 (Reuters) - Swiss private bank J. Safra Sarasin has agreed to buy Morgan Stanley's Swiss private banking unit, beefing up its business with the wealthy in the Middle East and Latin America.
The deal underscores the importance of size among private banks in Switzerland as a crackdown on tax evasion hits the industry, which provides tailored banking to wealthy individuals.
J. Safra Sarasin, formed in 2011 when Safra bought Basel-based Sarasin for 1.04 billion Swiss francs ($1.18 billion), said on Wednesday it would pay cash according to how many of Morgan Stanley's assets it could take on, but didn't disclose specifics on the price agreed.
The bank is buying roughly 10 billion francs in assets under management, with 130 client advisers in Zurich and Geneva, a source familiar with the Morgan Stanley unit told Reuters.
J. Safra Sarasin said it couldn't provide an asset figure.
The Swiss unit of Morgan Stanley has opted to work with U.S. officials in a Swiss government-brokered scheme to crack down on banks aiding wealthy Americans to evade taxes through hidden offshore accounts, according to the source.
A spokeswoman for Safra Sarasin said the bank wasn't acquiring any U.S. clients as part of the deal.
At Morgan Stanley, wealth management in the United States has gained in importance under the leadership of Chief Executive James Gorman in order to pay richer dividends.
In the wake of the financial crisis, Morgan Stanley agreed to buy Citigroup's Smith Barney business over time and merge it with its own wealth management unit, a process that began in 2009 and ended last year.
The Swiss sale follows changes made by Morgan Stanley to how it organised its private bank in Asia, for which Switzerland was originally intended as a platform to expand, according to the source. The Asian business is not included in the transaction.
The U.S. bank sold its wealth management arm in Europe, the Middle East and Africa with roughly $13 billion in assets to Credit Suisse more than a year ago.
$1 = 0.8836 Swiss Francs Reporting by Caroline Copley and Katharina Bart; Editing by Mark Potter