Washington socialite and free-lance journalist Selwa (Lucky) Roosevelt has been nominated as U.S. chief of protocol, the White House announced yesterday. The $58,500-a-year position carries the rank of ambassador.

"I'm thrilled and honored by the confidence this president has shown by nominating me," Roosevelt, 53, said last night. Her nomination requires Senate confirmation.

A staunch defender of First Lady Nancy Reagan, whom she first covered when Ronald Reagan was governor of California, Roosevelt becomes the fourth woman in a job that, until a few years ago, traditionally was held by men.

She is married to Archibald B. Roosevelt Jr., grandson of President Theodore Roosevelt and director of international relations for Chase Manhattan Bank. Her nomination, announced in Los Angeles where President and Mrs. Reagan are on a brief vacation, ends several months' speculation about who would succeed Leonore Annenberg. She resigned Jan. 1 after less than a year on the job, saying her husband, wealthy Philadelphia publisher Walter Annenberg, wanted her to spend more time with him.

Roosevelt is a native of Kingsport, Tenn. In 1950, she received a degree in international relations from Vassar College, where she was graduated with honors.

The White House announcement described her as "a Washington hostess" as well as journalist whose "beat" in the early 1950s, when she was on the staff of the now-defunct Washington Star, was a column titled "Diplomatically Speaking."

"I've observed the job for years and think it is one of the most exciting there is," said Roosevelt. "Covering state visits was one of my favorite jobs as a young reporter."

If confirmed as chief of protocol, Roosevelt's duties at the State Department will include arranging and implementing state and official visits by foreign heads of state and government and serving as liaison with the more than 140 nations represented by Washington's diplomatic community. She will assist the president, vice president and secretary of state in their personal and official contacts with the diplomatic corps here, as well as accompany the president on visits abroad.

In its announcement, the White House said Roosevelt "interrupted" her own writing career to accompany her husband, who was with the Central Intelligence Agency and later was an ambassador, on various diplomatic assignments abroad. They resided in Istanbul from 1951 to 1953, in Madrid 1958-'61 and London 1962-'67.

Fluent in Spanish, she has traveled widely on her own as a journalist, writing frequently for Town and Country (of which she is a contributing editor), McCall's and Family Circle, in whose current issue there is an article by her on alcoholism.

As a free-lance journalist for The Washington Post in 1968, she covered the Republican National Convention where Ronald Reagan, then governor of California, was first seen as a potential presidential candidate.

"I was assigned to cover Mrs. Reagan, though I'm sure she doesn't remember that," Roosevelt said last night.

The daughter of a Lebanese immigrant who came to the United States at the turn of the century, the former Selwa Showker was 16 years old when she began working as a cub reporter during summer vacations and after school for the Kingsport newspaper.

"I'd hardly set foot out of Tennessee until I went to college," she said of her childhood.

Reached by United Press International at her home in Johnson City, Tenn., last night, Roosevelt's mother, Najla Showker, said she did not find it unusual that her daughter should have been selected for the job.

"She is a very able person. She has led quite an interesting life, met all sorts of people. She knows how to handle herself."

Roosevelt, herself, said she was informed a few days ago by White House Deputy Chief of Staff Michael K. Deaver that she was being considered for the position. Shortly after that, she said, she also was telephoned by the first lady, whose life style and social awareness she had defended in an article written for The Washington Post's op-ed page last fall.

"She was as sweet as she could be and said she would be pleased and delighted if I accepted," said Roosevelt.

A self-described "good Republican (I always have been)," Roosevelt has written extensively about Embassy Row and the significance of Washington entertaining.

"I realize now that I probably have been preparing for this role all of my professional life," she said.

She called previous protocol chief Leonore Annenberg "supportive, so wonderful--I realize I'm going to have a hard act to follow."

At the State Department, acting protocol chief Tom Nassif, who had been among those mentioned as a possible candidate for the job, called Roosevelt's selection "outstanding."

"She's not a neophyte but has the background that will lend an added dimension to the job," said Nassif.

Roosevelt called her husband "the most supportive husband in the world" since the days when she was a young reporter covering the embassy beat.

"He says he is delighted to be prince consort," she said.

In Washington, where she has lived since 1967, she has been active in the Folger Shakespeare Library and the Children's Hearing and Speech Center of Children's Hospital. She is a member of the citizens advisory board of Duke University's comprehensive cancer center and recently joined the board of the American-Italian Foundation for Cancer Research.

She is the fourth woman to be named to the protocol post, all within the past eight years. Shirley Temple Black served under Gerald Ford and Edith (Kit) Dobelle under Jimmy Carter. By choosing Roosevelt as he did Annenberg, President Reagan has again reached into the inner circle of Nancy Reagan's friends.