Cardinal William W. Baum of Washington was named yesterday to the top Vatican post in charge of Catholic education institutions.

The appointment by Pope John Paul II will make Baum the highest-ranking American at the Vatican.

Baum, 53, who has been archbishop of Washington for nearly seven years and a cardinal for four, was named perfect, or head, of the Vatican's Sacred Congregation for Catholic Education.This agency of the Roman Catholic Curia, the church's top ruling council, has jurisdiction over most Catolic theological seminaries, church-affiliated colleges and universities and Catholic education below the college level.

A spokesman for the cardinal said he is expected to take "about a month" to wind up his work here and move on to his new position.

It is expected that it will take several months for the Vatican to select a success to head the church here, according to a spokesman for the apostolic delegate, the Vatican's representative in this country.

Baum's apppointment to the high Vatican post was not unexpected. Even since he was named a cardinal in 1976 at the unusually young age of 49, it was widely believed that he would eventually be assigned to Rome.

With his record of scholarship, his growing involvement in Vatican affairs,his fluency in Latin, Italian and French and his long friendship with the pope, Baum's credentials are unmatched.

Rumors that Baum was headed for a Vatican post increased last summer with the death of Cardinal John Wright, the only American in the church's highest council as head of the Vatican's Sacred Congregation for the Clergy. Although no church law requires that the Curia include an American, it makes good sense politically to include a representative of the third-largest church in worldwide Catholicism.

Baum will replace French Cardinal Gabriel-Marie Garrone, 79, who resigned to assume less demanding duties.

Baum, wearing bright scarlet robes and a cream wool surplice, talked to reporters at St. Matthew's Cathedral yesterday following the funeral of George Meany.

Asked whether he could have turned down the assignment, Baum said with a smile. "It's always understood that cardinal says 'yes' to a request of a pope.

Later in a homily at the noon mass at the cathedral, he called his summons to Rome an "indication of the will of the Lord."

Baum's appointment is in keeping with Pope John Paul's apparent policy of drawing the church's doctrinal wagons into a tightening circle.

The cardinal is a member of the Sacred Congregation for the Doctrine of the Faith, which in recent months has moved against theologians Edward Schillebeeckx, Jacques Pohier and Hans Kung. Baum's own pastoral messages have been models of Catholic orthodoxy.

Baum's overriding concern during his years here has been evangelism. "I have hoped to raise up as forcibly as I could the fundamental truths of the faith," he said yesterday, "to proclaim the truth about Jesus Christ . . . to proclaim the Gospel as fully as I could. That's what I attempt to do."

Although Baum issued pronouncements against racial discrimination during his time here, he has been criticized by activists within the archdiocese for not promoting programs of social concern.

Less than a year after he arrived here, he was criticized for purchasing a $525,000 house to live in. In the face of the criticism, he never lived in the house but sold it for a $25,000 profit for the church. Instead he purchased a $210,000 home in Spring Valley for his official residence.

Born in Texas and raised in Kansas City, Mo., Baum became an altar boy at 10 and a daily communicant at 12. He was educated in Catholic schools in Kansas City and in Rome.

When the Second Vatican Council was convened in 1962, he attended as theological advisor to Bishop Charles Helmsing of Kansas City and was assigned to work with the Secretariat for Christian Unity, where he helped draft the council's Decree on Ecumenism.

In 1964 the American Bishops named him director of their new Committee for Ecumenical and Interreligious Affairs, where he gained a worldwide reputation among Protestant and Eastern Orthodox church leaders, as well as Catholic church officials.

In 1970, he was named bishop of the tiny Missouri diocese of Springfield-Cape Girardeau where his ecumenical experiences served him well in the overwhelmingly Protestant community.

Baum's appointment to Rome opens a key spot on an increasingly complex ecclesiastical chessboard in this country. A vacancy already exists in St. Louis because of Cardinal John Carberry's retirement last summer. It is also expected that the Vatican may take steps to remove Cardinal John Cody as head of the troubled archdiocese of Chicago.

Church authorities must play to a number of constituencies in their search for a successor to Baum. In addition to strong largely white suburban parishes, the Washington archdiocese embraces a substantial number of black Catholics, as well as an even larger number of Hispanics.

In addition, there are a number of Catholics who feel that the head of this archdiocese should play an important role in voicing the church's concerns in the national area.