Lisle C. Carter, Jr., a former assistant secretary of the Department of Health, Education and Welfare and currently chancellor of the Atlanta University Center, has been named the first president of the University of the District of Columbia.

Ronald Brown, chairman of the university's board of trustees, announced yesterday that Carter accepted the post late Thursday night shortly after the trustees voted at a private meeting to offer him the job.

In mid-June, the trustees' first choice, Randolph W. Bromery, Chancellor of the University of Massachusetts at Amherst, turned down the post.

Carter could not be reached for comment yesterday, but his wife, Emily, confirmed in a telephone conversation that he will take the D.C. University post and is "excited" about it.

Carter, 51, a lawyer who graduated from Dartmouth College at age 18, was chief counsel for the National Urban League before coming to Washington in 1961 to serve in the Kennedy and Johnson administrations. He later was a professor of public policy and a vice president at Cornell University in Ithaca, N.Y.

Since January, 1974, Carter has served as the first chancellor of the Atlanta University Center, which was set up to manage joint programs, facilities and fund-raising for six predominantly black colleges with a combined enrollment of about 7,500.

Friends said yesterday that Carter's Atlanta job, which involves dealing with separate institutions, poses many problems similar to those facing him here. The new D.C. University is being formed by a merger of the city's three public colleges whose programs and faculties differ substantially.

The three colleges - Federal City College, Washington Technical Institute and D.C. Teachers College - had about 13,000 student last year. About 60 percent of them were part-time students.

Brown said yesterday that the administrative merger of the three schools would take place as scheduled Monday but that academic programs still are separate and will remain that way in the fall.

The university, which has an open-admissions policy, recently has been the focus of serious disputes about academic standards and about whether the school should emphasize liberal arts or vocational programs.

The university also has been involved in complicated negotiations with the City Council and Congress about its $51 million budget and its building program, now expected to cost about $1.33 million.

"One of the strengths Mr. Carter has will be in dealign with Congress because he has been an assistant secretary of HEW and also has had experience in fund-raising," Brown said.

Carter came to the Atlanta University Center shortly after it had been promised $20 million by the Ford Foundation. He has been involved in efforts to raise another $21 million for a new library, and friends said yesterday that Carter had been reluctant to leave Atlanta because all of the money needed for the library has not been collected yet.

Carter was born in New York City but spent most of his boyhood in Barbados where his father was a dentist and his mother a lawyer.

After graduating from Dartmouth in 1944, Carter served in the Army, then went to law school at St. John's University in Brooklyn.

During the 1950s, he spent two years as executive director of the Washington Urban League. When he served here in the federal government in the 1960s, he lived in Southwest Washington and in the Cleveland Park section of Northwest and sent his five children to public schools.

"He's an extremely good companion when he knows you well," one friend said yesterday, "but he has a little of that reserve that comes out of British school training. He's a very bright man, and he is challenged by the possibilities of what he might do here."