United Nations Ambassador-designate Andrew Young will leave Tuesday for a 10-day visit to Tanzania and Nigeria to confer with 15 black African leaders, the White House announced yesterday.

Young, due to be sworn in a White House ceremony early this afternoon, said last week he wanted "very much" to accept a personal invitation from Tanzanian President Julius K. Nyerere.

But any official decision on the trip, he said last week, would have to await the outcome of his confirmation hearings. He won easy Senate confirmation Wednesday.

The announcement brought to three the number of top-level Carter administration officials making diplomatic trips abroad in the early days of the new administration. Vice President Mondale is concluding a six-nation tour of Europe and Japan and Secretary of State Cyrus R. Vance leaves Feb. 14 for a six-country visit to the Middle East.

Young met for two hours yesterday with Carter, Vance, Zbigniew Brzezinski, the President's national security affairs adviser, and acting director of the Central Intelligence Agency, E. Henry Knoche, to coordinate foreign policy.

On another matter, Carter announced the temporary appointment of special assistant Joe Aragon as acting director of the Community Services Administration.

In making the announcement, Carter said the agency, which is supposed to aid various community action projects, "has become sluggish and politicized in recent years." He ordered Aragon to give him a detailed report within 10 days on what the CSA does with its $511 million appropriation and 1,059-member staff.