Robert L. Green, a dean at Michigan State University and a scholarly civil rights activist for almost two decades, was named president of the University of the District of Columbia last night.

The unanimous vote of 13 members of the UDC board of trustees came four weeks after the resignation of Benjamin H. Alexander after a stormy presidential term of less than a year. Board Chairman Ronald H. Brown said that Green, 49, had signed a five-year contract at a starting salary of $74,500, the maximum authorized by the D.C. City Council and $15,000 more than Alexander received.

Green, the dean of urban affairs programs at Michigan State and a prominent advocate of busing to achieve school desegregation, could not be reached for comment last night. But in a statement issued by a Detroit public relations firm, Green said he was accepting the UDC post as "the fulfillment of a lifelong aspiration."

The announcement said Green had resigned as president of City Communications Inc., a firm that is seeking a cable television franchise in Detroit. A week ago, Detroit Mayor Coleman Young recommended that the franchise be awarded to a competing company, a decision that is expected to be approved soon by the Detroit City Council. The statement said Green would continue to be chairman of the board of City Communications.

A day after Alexander announced his resignation as president on June 19, UDC board members said Green was the leading contender for the post. Last night, members said the board met privately with Green for several hours on June 17--two days before Alexander's resignation--and voted that day to authorize UDC Chairman Brown to "negotiate a contract of appointment" with Green. Brown said Green signed the contract last weekend, but added that Green had indicated "well before" then that he would take the job.

Brown said Green was the first choice of UDC's presidential search committee last year, but withdrew his name from consideration partly because of his interest in the cable-TV firm.

"All of us are extremely pleased that we could attract someone of the competence and caliber of Dr. Green," Brown declared. "We have been through several very trying months, but we come out of that unified. I think that will be reflected in our relations with our new president."

Alexander, a former president of Chicago State University, was named head of UDC last year by a 7-to-6 vote of the trustees. Five trustees joined a group of Faculty Senate leaders in an unsuccessful lawsuit to overturn the selection.

Last night's 13-to-0 vote for Green included all board members present. One seat on the 15-member board is vacant. Board member Vincent E. Reed, a former D.C. school superintendent who is a vice president of The Washington Post, was not at the meeting.

Last winter, amid strong opposition from faculty and administrators, Alexander's sweeping plan to trim and reshape the school administration was blocked by the board of trustees. Earlier, he had drawn criticism from faculty members--and praise from student leaders and community groups--for announcing publicly the decision to suspend and put on probation several thousand students with poor academic records.

Last night, Wilmer Johnson, president of the Faculty Senate who had been a critic of Alexander, praised Green as an "excellent choice."

"I think he will go about resolving problems with a much different style" than Alexander, Johnson said. "I think he will be much more supportive of shared governance . . . Running a university is the collective wisdom of a group of people. No one can come in and impose his views. You have to be very careful about that as a college president, and I think he has a greater feel for participatory decision-making."

At Michigan State, Green has been a professor of educational psychology since 1968. From 1973 to 1981, he served as dean of the College of Urban Development, an undergraduate program with about 120 students and eight professors. The college was abolished because of budget cuts.

In the 1960s, Green served as educational consultant to the Southern Christian Leadership Conference and was a close associate of the late Dr. Martin Luther King Jr.

He has been a critic of IQ testing and of using the Scholastic Aptitude Test (SAT) for college admissions. During the past decade, he has been a proponent of busing in his roles as a witness and a consultant in more than a dozen major desegregation cases, including in Chicago, Detroit and Richmond.

Last night, Brown said Green would take over as president of UDC on Sept. 1, but would work for a month before that as a consultant with interim president Claude A. Ford.

UDC, with about 14,000 students, has a budget of $72 million, about 570 full-time faculty members and about 1,000 other employes.

Brown said the board had "disccussed at length" the much-smaller scale of Green's previous administrative experience.

"We were impressed by the breadth and scope of his experience generally," Brown said. "We're confident he'll do very well here."