Frank Hodsoll, President Reagan's nominee for the chairmanship of the National Endowment for the Arts, was confirmed by the Senate yesterday afternoon. The vote was unanimous.

Hodsoll will begin his duties Friday when he chairs a quarterly meeting of the National Council of the Arts at the Four Seasons Hotel. The council is the advisory body to the National Endowment for the Arts.

"I'll be listening and getting an idea of how the council members feel about issues," said Hodsoll, who hopes to be sworn in Friday morning. Once on the job, he said, "my first priority will be personnel. I will start interviewing very shortly."

As predicted in September, when Hodsoll's name first surfaced as the likely nominee, he faced little opposition and was well received by senators despite his lack of arts administration experience.

Replacing Hodsoll as an assistant to White House chief of staff James Baker will be Jim Cicconi, a former general counsel to the secretary of state of Texas.

The White House is expected to announce soon its nomination of William Bennett, director of the National Humanities Center in North Carolina, for the chairmanship of the National Endowment for the Humanities. Sources on the Hill and in the White House said that the administration wanted to wait until Hodsoll was confirmed before announcing the choice of Bennett. The selection process for the NEH post has been fraught with controversy.