Ash, who had Parkinson's disease, died Dec. 14 at his home in Los Angeles, said his wife, Lila.
Through a series of acquisitions, Beverly Hills-based Litton Industries became one of the fastest-growing conglomerates of the 1950s and '60s, a highly diversified and multinational company whose products ranged from manufacturing electronic typewriters and industrial microwave ovens to producing electronic guidance systems for aircraft and building ships.
Ash, who began as the company's chief fiscal officer, became president in 1961.
Litton Industries was one of the nation's largest military contractors by 1968, the year Ash became an advisor to President-elect Richard Nixon on ways to improve management and efficiency in the federal government.
Not long after Nixon took office in 1969, he chose Ash to head a new "and thorough" review of the organization of the executive branch. Ash served as chairman of the six-member President's Advisory Council on Executive Organization for two years.
One of the recommendations made by the so-called Ash Council was the plan that created the Office of Management and Budget out of the former Bureau of the Budget.
In late 1972, Ash resigned as president of Litton Industries after Nixon announced that he would appoint him as director of the Office of Management and Budget, succeeding Caspar W. Weinberger.
Ash continued as budget director for several months under President Ford and resigned in late 1974.
Asked if he had brought "radical changes to government," Ash said in a 1977 Los Angeles Times interview that he "contributed two or three innovations. If they have a lasting effect, I'll consider myself enormously successful.
"One was to create the Office of Management and Budget out of an agency that had been traditionally the Bureau of the Budget. The object was not to build an empire. I'm one who believes the least government is the best government. My goal was to impose managerial responsibility on the spending of more than $300 billion a year.
"As director of OMB, I wanted to bring in a concept that no matter how awesome its size, government can be made more effective by using management techniques."
In 1976, Ash was named chairman and chief executive of Addressograph-Multigraph Corp., a Cleveland-based major manufacturer of duplicating and other business machines. It was renamed AM International in 1979.
After he resigned from the company in 1981, Ash and his wife divided their time between Los Angeles and Virginia, where they bought three farms.
In the early '80s, Ash also served as vice chairman of the Los Angeles Olympic Organizing Committee and was chairman of its finance commission.
The son of a Los Angeles hay and grain broker, Ash was born on Oct. 20, 1918.
An early flair for numbers allowed him to graduate from Manual Arts High School, where he was the youngest and shortest member of his class, at age 16.
"Partly because my youth and height made me acutely shy, partly because my parents didn't insist on college, I passed up further studies and began looking for work," he recalled in a 1977 Times interview.
He landed a job as a cash-collection messenger at Bank of America in downtown Los Angeles. After moving to the El Monte branch, he was promoted to bookkeeper, teller and operations officer.
Ash joined the Army Air Forces as a private shortly after the Japanese attack on Pearl Harbor and rose to the rank of captain while serving in the Statistical Control Service.
Ash, who had been assigned to Harvard Business School as an officer candidate and later returned as a statistical management expert, had his undergraduate requirements waived at the school after the war. He finished first in his class and earned a master's degree in business administration in 1947.
Ash served on a number of boards of directors, including Bank of America Corp. He also was a member of the board of the Music Center, the Music Center Foundation and the Los Angeles Opera, of which he was chairman for five years.
In 2003, the Ashes endowed the Roy and Lila Ash Center for Democratic Governance and Innovation at the John F. Kennedy School of Government at Harvard University.
In addition to his wife of 68 years, he is survived by his sons, Charles, James and Robert; his daughters, Loretta Danko and Marilyn Hanna; nine grandchildren; and two great-grandchildren.