The Commission on the Bicentennial of the U.S. Constitution, which is chaired by the chief justice of the United States, has chosen its executive director -- the chief justice's administrative assistant.

The commission announced yesterday that Mark Cannon, who has been Warren E. Burger's top aide since 1972, will assume the job, which pays $86,200 a year.

A five-member search committee, which did not include Burger, said it reviewed 150 applications.

"Although there were many qualified candidates, Dr. Cannon was the search committee's unanimous selection," said Betty Southard Murphy, who headed the searchers. "We were able to persuade the chief justice to release Dr. Cannon because of the commission's need to get off to a fast start" for 1987.

Previously, Cannon was with the Institute of Public Administration in New York, a private think tank; a congressional staffer, and chairman of the political science department at Brigham Young University.

A commission statement noted that its executive director is one of only 16 executive branch positions that pays $86,200; all but two of those persons are members of the president's Cabinet.

Under its authorization, the commission can hire six staffers with appropriated funds; up to 20 staffers can be loaned from agencies and the salaries of up to 40 staffers can be paid with private funds.

In January, before President Reagan appointed the commission's members, the White House installed former senator Roger W. Jepsen (R-Iowa), who had just lost his Senate seat, as the commission's executive director. Jepsen's administrative assistant, Donald E. Johnson, became his deputy.

But the commission's authorizing legislation specified that the panel, not the president, was supposed to pick the commission's executive director. Three months later, Jepsen was named chairman of the National Credit Union Administration.