After a search lasting nearly five months, President Reagan announced yesterday that he will nominate William S. Sessions, chief judge of the U.S. District Court for the western district of Texas, to be director of the Federal Bureau of Investigation.

In a brief statement on the south lawn of the White House, Reagan said Sessions "is well-recognized as a man of great personal integrity and honor, dedicated to the vigorous enforcement of the criminal laws . . . and the even-handed administration of justice."

Reagan, accompanied by Attorney General Edwin Meese III, former FBI director William H. Webster, now head of the Central Intelligence Agency, and White House chief of staff Howard H. Baker Jr., said Sessions has "established himself as a fair-minded, tough prosecutor . . . committed to protecting the rights of all Americans under the Constitution."

Sessions, who has a tough law-and-order reputation, thanked Reagan and said, "I look forward to trying to maintain the high standards that Judge Webster has provided."

The announcement came after Sessions, 57, met earlier in the day with Reagan and Meese after flying here Thursday night from his home in San Antonio.

His nomination to the 10-year term as FBI director follows a lengthy and politically embarrassing search by the Reagan administration in which several candidates, including former deputy attorney general D. Lowell Jensen, turned down the job. Webster was nominated to head the CIA in early March and was confirmed May 19.

Administration officials had complained that Meese was taking too long to find a replacement for Webster. The slowness of the process, according to one official, "gave a public impression of paralysis that was damaging to the president."

But Meese said, "Considering the enormity of the task, I don't think it took very long at all." He said more than 60 people were considered for the job.

Sessions, born in Fort Smith, Ark., received his undergraduate and law degrees from Baylor University. The son of a minister, he was in private practice for 10 years in Waco, Tex., before being appointed a federal prosecutor by President Richard M. Nixon. He was named to the federal bench in 1974 by President Gerald R. Ford.

He gained national attention in 1982 and 1983 by presiding over two trials stemming from the killing of U.S. District Court Judge John H. Wood Jr., known as "Maximum John" for the tough sentences he imposed on drug dealers.

John C. Lawn, who headed the FBI's San Antonio office and worked with Sessions during the Wood investigation, called him "an outstanding nominee. He's a no-nonsense person." Lawn, now head of the federal Drug Enforcement Administration, said Sessions is known for giving "great attention to detail and being very demanding of his subordinates. . . . He's ideal for the job."

Sessions served as U.S. Attorney in San Antonio from 1971 until 1974. He also worked for the Justice Department here from 1969 to 1971 as a deputy assistant attorney general in the criminal division, where he led nearly 20 prosecutions of alleged campaign spending irregularities by businesses and unions.

Wilmer Haley, who worked with Sessions in the mid-1960s in a Waco, Tex., law firm, yesterday described his former law partner as having the "abilities and moral qualities to do the job. His integrity is absolute."

Haley, a Democrat, said Sessions was a Republican "back when it wasn't popular in Waco to be a Republican." But he added that Sessions was never particularly active in politics. "He's not a political animal," Haley said.

Other than his tough sentences in criminal cases, Sessions' court rulings do not break down along clear ideological lines.

In 1977, he ordered the El Paso Independent School District to redraw some boundaries in a desegregation case, but a year later he angered some Hispanic groups when he ruled that employers could forbid their workers from speaking Spanish on the job.

He angered the news media in 1982 when he barred reporters from interviewing jurors in the Wood murder case, a ruling that was at least partially overturned later. But the previous year, Sessions overturned a state order and allowed a small monthly newspaper to print the names of the client list of a local house of prostitution.

Sessions, a Republican who is highly regarded by members of both parties, is not expected to have serious difficulty winning Senate confirmation.

Senate Judiciary Committee Chairman Joseph R. Biden Jr. (D-Del.) reacted cautiously, saying that he "needs to become acquainted with" Sessions' record. But he said that based on his first impression, the nomination can be considered expeditiously.

Sen. Lloyd Bentsen (D-Tex.) said in a statement, "I've known Judge Sessions for many years and think highly of him. He'll do an excellent job as director of the FBI, and I intend to use what influence I have to send his nomination through the Senate as quickly as possible."