Chiu, 42, was re-elected to the position by his fellow supervisors in a unanimous vote after retaining his District 3 seat in November's election.
The board president serves a two-year term and is in charge of appointing chairs and members of board committees and running the full board's regular meetings.
Supervisors Jane Kim and Malia Cohen were also nominated for the position, but both withdrew their nominations just before the vote.
Also at today's meeting, San Francisco Superior Court Presiding Judge Cynthia Ming-mei Lee swore in all of the supervisors who were elected or re-elected in November's election.
Chiu, Eric Mar, David Campos and John Avalos were re-elected, while London Breed and Norman Yee won their first terms on the board.