The Senate Judiciary Committee unanimously voted yesterday to approve the nomination of William S. Sessions, a federal judge from Texas, as director of the FBI.

Taking a short break from the contentious opening-day hearing on Supreme Court nominee Robert H. Bork, the committee voted without objection to send Sessions' nomination to the full Senate with a recommendation that it be approved. The Senate is expected to approve Sessions by an overwhelming margin later this week.

Sessions, 57, has been widely praised for his reputation for toughness and fairness during his years as U.S. attorney and chief judge of the U.S. District Court in San Antonio.

"Judge Sessions' record demonstrates that he is a tough but fair-minded man, whose experience, intellect and character qualify him to lead the Federal Bureau of Investigation," the committee concluded in an eight-page executive report sent to the full Senate.

The report also said that Sessions' record "demonstrates a sensitivity to individual rights and civil liberties, an important qualification for the director of the FBI."

"Judge Sessions' extensive law enforcement experience, his commitment to the rule of law and his strong moral character exemplify the type of person who should lead the FBI," said Judiciary Committee Chairman Sen. Joseph R. Biden Jr. (D-Del.). Biden added that he expects the full Senate to move quickly to confirm Sessions.

Sen. Edward M. Kennedy (D-Mass.) said Sessions was an "outstanding choice" to succeed William H. Webster. After nine years as FBI chief, Webster left in May to become director of the Central Intelligence Agency after the death of William J. Casey.

No one opposed Sessions at his one-day confirmation hearing last week, and the senators on the committee had predicted his easy confirmation for a 10-year term. Sessions was nominated July 24 by President Reagan after a five-month search.

At his confirmation hearing last Wednesday, Sessions testified in response to questions related to the Iran-contra scandal that he would guard FBI independence and would refuse to obey a presidential order he considered improper.

Sessions said he would not, however, use "the shield of resignation" in any dispute with the president.

Sessions said he has been given a verbal guarantee by Attorney General Edwin Meese III of the FBI's freedom to conduct investigations free of political pressures.