The Rev. Timothy S. Healy, who has led Georgetown University for 13 years, announced his resignation yesterday to become president and chief executive officer of the New York Public Library. Healy, 65, will become head of one of the world's largest research libraries, as well as a library system that operates 82 branches around New York City. In letters to Georgetown's faculty and students, Healy said he had decided to resign at the end of the university's bicentennial celebrations in the fall, believing that Georgetown "would benefit from a new and younger imagination in this office." Besides filling Georgetown's campus with new buildings and raising its endowment fivefold, Healy has been a major national spokesman for higher education. He has served as board chairman of the American Council on Education, the umbrella group of U.S. colleges, and as chairman of the National Association of Independent Colleges and Universities. He also has been at the center of sharp debate over Georgetown's position as the nation's oldest Catholic university and over its relations with the federal and District of Columbia governments, from which the university has received special appropriations and tax-exempt bonds. Last year, despite pleas from alumni groups and Washington's Catholic archbishop, Healy took the lead in having Georgetown settle a lawsuit by gay student groups under which the university agreed to follow a D.C. Appeals Court order, requiring it to provide equal treatment and a subsidy to gay groups. David Riesman, a Harvard University professor who has written extensively on U.S. universities, said yesterday that Healy "has been a presence in Washington. He's been a presence in the Jesuit order. He's been a presence in American higher education. He's done exemplary, vivifying work." He succeeds Vartan Gregorian, 54, who is leaving the library to become president of Brown University, often a rival of Georgetown for prestige and students. Healy, who was born and reared in Manhattan, described the public library yesterday as "the people's university" and praised "its tradition of openness to all people . . . . Everything I have done in higher education so far strikes me as preparation for this task." In an earlier interview, Riesman said that over the past two decades, under Healy and his predecessor, the Rev. Robert J. Henle, Georgetown has become the only one of the nation's 230 Catholic colleges and universities to enter the small circle of "elite, high-prestige" schools. It is also the Catholic university with one of the smallest proportions of Catholics -- about 60 percent among undergraduates, about half among faculty and less than half among graduate and professional students. Healy often has emphasized Georgetown's religious "pluralism," and in 1979 he issued a directive ordering that references to the Trinity be dropped from prayers at graduation and other compulsory university functions. In a letter explaining the decision to settle the gay student case, Healy said he wanted to "pull . . . {the Georgetown} community back together" after a "long and divisive" eight-year court battle. He said the university "has really been made to pay" for trying to uphold Catholic teaching against homosexual practices, noting that the District government had refused to authorize tax-exempt bonds for university construction. In December, the D.C. Council authorized the sale of $237 million in bonds after Healy telephoned council members with assurances that Georgetown would continue to give equal treatment to gay groups even if the city's antidiscrimination law is overturned by congressional action. "He's a pragmatist doing what is best for the institution," one faculty member said. Healy has been a major advocate of expanded enrollment of minorities, particularly blacks, who now make up 9 percent of Georgetown's freshman class, which is about 20 percent minority overall. He also has promoted student-run service programs to aid low-income students in the District's public schools, and has been a major supporter of Georgetown's basketball program, which has won national championships but encountered some faculty criticism for lowering admissions standards. Last month, Healy joined basketball coach John Thompson in criticizing an NCAA rule setting minimum admission test scores as unfair to blacks. Throughout his 13 years as Georgetown's president, Healy has taught small undergraduate seminars in English literature, often focusing on the poetry of John Donne, the subject of Healy's doctorate at Oxford University. He also has regularly led Shakespeare reading groups for medical students. A poll of higher education leaders in 1986 rated Healy as among the five "most effective" university presidents in the country. Students in his classes praise Healy warmly. However, yesterday a student newspaper, the Georgetown Voice, said Healy has been "much criticized by students and faculty for being inaccessible." "He's not a buddy. He can be kind of aloof," said one former administrator who knows Healy well. "He can swear like a marine, and he really can be an s.o.b. to his staff. But he is a guy who would bite the bullet in favor of quality. He would make the tough decisions." These have included closing the Georgetown Dental School, terminating a group of weak doctoral programs, severing the university's ties with the Center for Strategic and International Studies and returning a $600,000 gift from Libya after four years of intermittent public criticism. Healy describes himself as a Democrat and has delivered prayers at party functions. He sharply criticized the Reagan administration for fostering "a bout of meanness" which he said was "souring" American society. In an interview several years ago, Healy called himself "a professional New Yorker." Before coming to Georgetown, he taught English at Regis High School in Manhattan and at Fordham University in the Bronx. For seven years he put on a business suit, though remaining a priest, and served as vice chancellor for academic affairs at the City University of New York. "Now he's going home to New York, and he's going home to books," university spokesman Gary Krull said yesterday. "He told me it was thrilling that anyone would want a 65-year-old person like him for the job he's getting."