Archbishop Joseph L. Bernardin of Cincinnati will succeed the late Cardinal John Cody of Chicago as head of the nation's largest archdiocese, the Vatican said yesterday.

Bernardin, who at 54 has served both as general secretary and president of the U.S. Catholic hierarchy, has a reputation as a progressive on social issues and a traditionalist on theology. But of importance to the dissension-wracked Chicago archdiocese is the fact he is regarded as an effective administrator and a patient arbiter of differing viewpoints.

The announcement ends years of speculation on a successor to Cody, whose authoritarian style had caused the archidiocese to be wracked by turmoil long before allegations of his financial wrongdoing were made public last fall.

The bitter 16-year battle between the cardinal and his priests were more damaging to the church than the disclosure that a federal grand jury was investigating charges that Cody had channeled church funds illegally to a woman he identified as a step-cousin. The charges were dropped after Cody's death April 25 at the age of 74.

The disputes, combined with Cody's deteriorating health, tended to put leadership of the archdiocese on automatic pilot. "It's like waiting for the White Sox to win the pennant," one priest observed earlier this year.

No date has been set for Bernardin's formal installation as spiritual leader of the 2.4 million Chicago Catholics, but the church usually makes such moves within weeks after the appointment is announced. The Chicago appointment carries with it virtual assurance of elevation to cardinal.

According to church sources, Bernardin was summoned to Rome and notified of the appointment by Pope John Paul II privately last Monday, although the appointment was not made public until yesterday morning. The pope is said to be a friend of Bernardin, with whom he once served on a key Vatican planning committee.

"I am deeply moved by the confidence the Holy Father has placed in me by appointing me archbishop of Chicago," Bernardin said in a statement released through aides in Cincinnati. A spokesman for the archbishop said Bernardin, who reportedly left Rome yesterday, will remain in seclusion until a press conference in Cincinnati tomorrow morning.

Bernardin--the name is pronounced with the accent on the first syllable--has long been considered a favorite to succeed Cody. But some feared he might be tainted by the disclosure last fall of a bizarre plot by priest-novelist Andrew Greeley. It would have ousted Cody and replaced him with Bernardin who, Greeley contended in a diary he kept in the mid-1970s, could be manipulated in an effort to control the 1978 papal election.

Bernardin dismissed the Greeley plot as a "fantasy." The Vatican apparently agreed with the judgment of one churchman, who knows both men, that Bernardin "has no more responsibility for his appearance in Andy Greeley's dream than Jodie Foster has in John Hinckley's."

The soft-spoken and amiable Bernardin is something of a wunderkind of American Catholicism. Born of Italian immigrant parents in Columbia, S.C., he rose rapidly in a hierarchy dominated by Irish-Americans from the Catholic population centers of the North and Northeast.

He did his priestly studies in this country--St. Mary's Seminary in Baltimore and Catholic University here--instead of at one of the institutions in Rome that have long been considered a pathway to the episcopacy.

In 1966, at 38, he became the youngest bishop in the country when he was made an auxiliary to the late Archbishop Paul Hallinan of Atlanta.

Two years later, Bernardin was called to Washington as general secretary of the bishops' conference during a pivotal period as the Catholic Church sought not only to work out the reforms of Vatican II within its ranks but also to form new ecumenical relationships with other churches.

One measure of his success in helping shepherd the American church through those turbulent times was his election by fellow bishops, after he had been made Archishop of Cincinnati in 1972, as president of the bishops' conference.

The American bishops also repeatedly chose him to represent them at Synods of Bishops in Rome, where Bernardin eventually ended up on one of the key planning committees with then-Cardinal Karol Wojtyla, now Pope John Paul II.

Bernardin is also a member of the Pontifical Commission for the Revision of the Code of Canon Law, the international committee charged with the sensitive task of updating the church's complex legal code.

Bernardin is also chairman of the committee which has proposed to the American hierachy a position statement on nuclear warfare. It would put the church on record as saying there are virtually no circumstances under which the use of nuclear weapons is morally defensible.

The bishops will act on the proposed statement at their annual meeting here in November.

In Chicago, news of the new archbishop was well received. Msgr. John R. Keating, interim administrator of the Chicago archdiocese, in a mass at Holy Name Cathedral offered a prayer of thanks "for the gift of our new shepherd" and pledged "our devotion, our love and our fidelity."