President-elect Ronald Regan will nominate Utah education commissioner Terrell Bell to become secretary of education, filling the last vacant department job in his Cabinet, it was learned yesterday.

The selection of Bell, who served in the Ford administration, is expected to be made public this week, barring any hitch in his security and other clearances.

Yesterday Reagan broke his tradition of not appearing with his choices for high administration posts by walking down the steps of Blair House to present James S. Brady and Karna Small to reporters as his press secretary and deputy press secretary.

It was a courteous launching for Brady who, with good humor and grace, has been acting as press secretary and made no bones about wanting the White House press job, while Reagan aides sounded out a number of others for the post.

Bell, 59, met with Reagan for 30 minutes at Blair House yesterday and they discussed the fate of the Education Department which Reagan pledged during the presidential campaign to abolish.

It appears that a consensus is building among Reagan's advisers that the department should merely be reduced from Cabinet rank and made an independent body similar to the National Aeronautics and Space Administration or the National Science Foundation.

Also, some advisers and Republican members of Congress favor restoring the Pentagon's responsibility over overseas schools for American dependents.

It is not clear, however, what will happen to the Education Department's Civil rights division, which has been at the center of controversies over school desegregation, sex discrimination, bilingual education and opportunities for handicapped students.

Bell was U.S. commissioner for education from June 1974 to August 1976 under Caspar Weinberger, who then was head of the Department of Health, Education and Welfare and who is slated to become Reagan's defense secretary.

Bell's return to the federal government was pushed by Sen. Orrin Hatch (R-Utah), and little opposition to his nomination is expected although he has taken some potentially controversial positions.

One was his support for creation of the separate Education Department that he now will be asked to reduce. Bell associates say, however, that his aim was to take education out of HEW, not necessarily to create a new Cabinet-level department.

As education commissioner, Bell approved in 1975 the guidelines that have been used to press hundreds of school systems into starting bilingual programs for children who have little or no command of English.

A spokesman for Hatch said "the senator is extremely pleased at the choice of Bell, who has extensive experience at both the federal and state level." Hatch's candidate to be labor secretary. Betty Murphy, was passed over by Reagan in favor of New Jersey contractor Ray Donovan.

Reagan and his chief of staff designate, James Baker III, stressed to reporters that the press secretary's importance would not be reduced in the Reagan administration and they said Brady would have access to the president "no less than once a day."

"I have never run an administration where people did not have access. I guarantee it," Reagan said.

Baker said the press secretary will not be downgraded and will play the traditional role inside the White House. Brady will report to Baker, according to the White House table of organization.

Reagan was asked jokingly whether Brady is "good-looking enough for the job." The Washington Post reported last week that Nancy Reagan insisted that the press secretary be "reasonably good-looking."

"I am getting to be an irate husband at some of the things I am reading, none of which are true," Reagan said. He declined to name other articles quoting his wife that angered him, but said the quote about the press secretary's looks "is a total invention out of whole cloth."

Then Reagan smiled and said: "Nancy couldn't be more delighted -- she thinks he's absolutely handsome."

Brady, 40, was director of public affairs and research for the Reagan campaign. He joined Reagan after the campaign of John B. Connally, for whom he was press secretary, collapsed.

Brady is a graduate of the University of Illinois and worked for a year on the staff of the late Everett M. Dirksen, who was Senate minority leader. He has worked for the House of Representatives as a communications consultant, for the Department of Housing and Urban Development, the Office of Management and Budget, the Pentagon and Sen. William V. Roth (R-Del.).

Small, a graduate of the University of Michigan, has been moderator of a U.S. Chamber of Commerce public affairs program called "It's Your Business." She has also been a television anchorwoman, most recently for WTTG here.

Larry Speakes is expected to be named another deputy press secretary soon, according to well-placed sources. Speakes was an assistant press secretary in the Ford White House and worked on press relations for the Reagan campaign.

Reagan stayed in Blair House all day, meeting with Gen. Alexander M. Haig Jr. and Richard S. Schweiker, his choices to become secretary of state and secretary of health and human services, respectively. Reagan also hosted a group of women leaders who supported his campagin, and gave a reception for the California Republican congressional delegation. Last night, he made a brief appearance at a Hoover Institution dinner and was guest of honor at a dinner given by Time Inc.