Ron Klain, the White House chief of staff who has steered President Biden’s administration through two years of triumphs and setbacks, is expected to step down in coming weeks in the most significant changing of the guard since Mr. Biden took office two years ago.

Mr. Klain has been telling colleagues privately since the November midterm elections that after a grueling, nonstop stretch at Mr. Biden’s side going back to the 2020 campaign, he is ready to move on, according to senior administration officials, and a search for a replacement has been underway.

The officials, who discussed internal matters on condition of anonymity, would not say whether a successor has already been picked or when the decision would be announced, but indicated that it would come at some point after the president outlined his agenda for the coming year in his State of the Union address on Feb. 7.