Federal magistrate Elsie L. Munsell is President Reagan's choice to become the next U.S. attorney in Alexandria, the White House announced yesterday.

If confirmed by the Senate, Munsell, a 42-year-old Republican, will be the first woman to hold the $50,100-a-year post in Virginia.

"I think history is being made," said Sen. John Warner (R-Va.), who recommended Munsell, after a three-month search for judicial and prosecutor candidates. He said Munsell was "unquestionably one of the most outstanding, professional people" he had interviewed for the job.

Warner, who stressed repeatedly he was searching for women and blacks to recommend for federal judicial positions, said he had discussed a judgeship with Munsell, but that Munsell felt she needed more experience.

Munsell said she got the news in a note handed to her on the bench yesterday as she conducted a jury trial in Alexandria. She will replace Justin Williams, who has headed the office since June 1979.

A 1972 graduate of the Marshall Wythe School of Law at The College of William and Mary, she worked for a year as an assistant prosecutor in Alexandria before joining the same U.S. Attorney's office she will soon head if approved by the Senate.

Munsell was chief of the office's civil division before becoming a magistrate in 1979. Her husband, George Williams, currently holds the same position in the federal prosecutors' office and will be leaving upon her appointment, Munsell said yesterday.

Warner said that decision, which he called a "tremendous sacrifice," was made before he submitted Munsell's name to Justice early in the summer.

Also on Warner's list for the prosecutor's job were William F. Davis, 59, chairman of the Suffolk school board; Frank W. Dunham Jr., 38, of Alexandria, an attorney; Kenneth L. Foran, 39, of Alexandria, former counsel to the Senate Judiciary Committee, and Barry R. Poretz, 37, a former Alexandria assistant prosecutor.

Warner said yesterday he understood from the White House that the name of Fairfax Circuit Judge James C. Cacheris is "moving ahead quite favorably" for a vacancy on the federal bench in Alexandria. He declined to say when Cacheris' name might be placed in nomination by the president.

White House counsel Fred Fielding attributed any delay to a policy of waiting for FBI checks.