NEW YORK, AUG. 9 -- The New York Stock Exchange, eager to find a new chief with experience in Washington as well as on Wall Street, announced today that former undersecretary of state William H. Donaldson will become the Big Board's chairman and chief executive on Jan. 1.

Donaldson, 59, is head of the investment firm Donaldson Enterprises Inc. He will succeed John J. Phelan Jr., who is stepping down to pursue other interests after a tenure highlighted by his widely praised handling of the Black Monday market crash in October 1987.

Donaldson, in his new position, is expected to preside over the introduction of round-the-clock trading and over the exchange's ongoing adjustment to a more international and computer-driven marketplace.

Acknowledging that the stock market's reputation had suffered somewhat in what he called "the era of greed" in the 1980s, Donaldson said that one of his biggest challenges would be "restoration, maintenance and building of public confidence in the NYSE as the best market in the world."

To achieve that goal, Donaldson said in a telephone interview, he hopes to spend "a lot of time" working with Congress and the administration to "bring the level of mutual understanding up to the point where we don't make mistakes legislatively" in trying to regulate the market.

"This marketplace, for all its warts and pimples, is a pretty efficient operation," Donaldson said.

Donaldson made his name in the securities industry as a founder of the Donaldson Lufkin Jenrette Inc. investment firm. He also served as an adviser to vice president Nelson Rockefeller and was the founding dean of the Yale Graduate School of Management, a business school oriented toward public policy.

The other leading candidate for the chairman's job had been Richard A. Grasso, NYSE president and chief operating officer. Grasso will become executive vice chairman of the Big Board in January.

While Grasso, 44, has been at the exchange for 22 years, Donald S. MacNaughton, chairman of the special search committee that nominated Donaldson, made clear that the Big Board wanted someone with experience in government as well as in the securities industry. The committee looked for someone with "breadth of experience beyond the marketplace itself," MacNaughton said.