The White House yesterday put an end to months of speculation and rumor by announcing its intention to nominate Peace Corps Deputy Director Edward A. Curran as chairman of the National Endowment for the Humanities.

Curran, 51, had been considered the most controversial of the half-dozen names that circulated in recent months as possible successors to former chairman William Bennett, who left the endowment earlier this year to become secretary of education.

Curran made headlines three years ago as director of the National Institute of Education when he wrote to President Reagan suggesting the abolition of his own agency. Curran clashed with his boss, former secretary of education Terrel Bell, over the incident and resigned soon after. The letter, however, earned him praise from some conservative columnists and lobbying groups.

His stint at the Peace Corps has been stormy, according to friends and colleagues, who say that he often has been at odds with Peace Corps Director Loret M. Ruppe on agency policy.

News of Curran's nomination was greeted with reserve by a ranking Republican lawmaker on the Senate committee that must approve Curran's name before sending it on to the full Senate.

"I have not made up my mind on Mr. Curran and will examine his credentials when he comes before the committee," said Sen. Robert T. Stafford (R-Vt.), a member of the Labor and Human Resources Committee.

President Reagan reportedly had approved the Curran nomination at least two months ago, but it had been stalled by administration moderates searching for a less controversial, more moderate choice. Leaders of the museum, university and scholarly groups that represent many of the recipients of endowment money had expressed fears that Curran lacked the experience and temperament required to preside over the endowment.

Stafford himself had put a hold on the nomination for a few weeks by notifying the White House that he had questions about Curran's philosophies, according to a Stafford spokesman.

Curran could not be reached for comment but released a statement saying he was "proud" that the president had chosen him and that he "looked forward to serving the President and the American people."

Lisa Phillips, executive director of the Humanities Alliance, a trade organization for many of the nation's universities, learned societies and museums, said the members of her organization are interested in learning more about Curran's views.

"We hope for in-depth Senate hearings," Phillips said. " Curran , of course, is different from previous NEH nominees in that he does not come from higher education and does not have a demonstrated knowledge of public programs that do not involve schools." Phillips described the nomination as "sensitive" because of the great discretion the endowment's chairman exercises over funding priorities.

The National Endowment for the Humanities is a federal agency with an impact and visibility far greater than its relatively small $140 million budget, and the periodic search for its chairman usually produces political fireworks.

The endowment awards thousands of grants and fellowships to scholars, museums and universities for research and preservation. The chairmanship has often served as a pulpit for administrations' views on the role of the liberal arts in American life.

Bennett, for example, used the endowment to call for a return to the study of the classics of western history, literature and philosophy. He is described by friends and critics alike as having steered the endowment away from the cultural pluralism that marked the Carter years.

The Massachusetts-born Curran was headmaster of the National Cathedral School from 1968 to 1980. He subsequently served on President Reagan's Education Transition Team and put in one year as associate director of the Office of Presidential Personnel. In 1980 he headed a political group called Professionals for Reagan, and is, according to friends, a close friend of Vice President George Bush.

Curran graduated with a bachelor's degree from Yale University in 1955 and earned a masters' degree from Duke University in 1968. He was dean of students at a Houston private school from 1957 to 1968, and taught at a private boys' school in Englewood, N.J., for two years before that.