Benno C. Schmidt Jr., the dean of the law school at Columbia University, will be named president of Yale University today, according to sources at the Yale Law School.

Schmidt, an "Old Blue" Yale alumnus, would become the 20th president in the university's 284-year history.

He would be taking over one of the most prestigious jobs in higher education in the United States.

Yale officials have scheduled a news conference this morning to announce the name of the successor to A. Bartlett Giamatti, who has been Yale's youngest president.

Giamatti unexpectedly decided to step down next June, after eight years dedicated largely to restoring the school to fiscal health.

Schmidt's choice would continue the Yale Corp.'s pattern of selecting a renowned scholar from among Yale alumni as the university's president.

Schmidt, 43, was graduated from Yale College in 1963 and from the Yale Law School in 1966.

After law school, he served as clerk to Chief Justice Earl Warren.

Schmidt has written extensively on constitutional law, freedom of the press and First Amendment issues since he joined the Columbia faculty in 1969.

Schmidt was named the dean of Columbia University's law school in July 1984.

He has become known to television viewers from his appearances on the PBS show "The Constitution: That Delicate Balance."

Yale's presidential selection process, which began when Giamatti announced last April that he would step down, has been cloaked in the sort of pomp and secrecy usually reserved for the selection of a new pope.

As a result, the search committee, headed by former secretary of state Cyrus R. Vance, has been able to avoid the kind of embarrassing press leaks that plagued the university's previous search.

That time, three other candidates turned down the job before the Yale Corp. in December 1977 settled on Giamatti, who was then 39.

Last Friday, the search committee was reported by the Yale Daily News to have settled on a list of about seven candidates, and members of the committee went to New York over the weekend to talk with Schmidt.

Other candidates on the final list included:

Vartan Gregorian, the president of the New York Public Library; Maxine F. Singer, the head of the biochemistry laboratory at the National Cancer Institute in Bethesda; Guido Callabresi, the dean of Yale's law school, and Yale history professor Gaddis Smith.

The next president of Yale will take over an institution that is financially afloat, after Giamatti's efforts erased the school's $16 million in operating losses.

Giamatti also had become a forceful advocate for higher education, at a time of federal cutbacks in aid to education.