WASHINGTON—The Senate confirmed William Barr as attorney general Thursday, putting the veteran of corporate and Washington legal circles in charge of a Justice Department that has been rocked by departures, political storms and the special counsel’s Russia investigation.

Mr. Barr, who served as President George H.W. Bush’s attorney general in the 1990s, was sworn in during a White House ceremony later Thursday and was expected to get to work with meetings early Friday.

Three Democrats—Sen. Doug Jones of Alabama, Sen. Joe Manchin of West Virginia and Sen. Kyrsten Sinema of Arizona—joined Republicans in a the 54-45 vote to confirm Mr. Barr. Sen. Rand Paul of Kentucky was the sole Republican “no” vote.

Democrats had expressed concerns over how Mr. Barr would manage Robert Mueller’s investigation into Russian interference in the 2016 presidential election and whether Mr. Barr would make its conclusions public.

Wrestling with whether to release the Mueller probe’s findings will likely be among Mr. Barr’s first tasks. Mr. Barr emerged from his confirmation hearing vowing to bring as much transparency as possible to those findings, but he stopped short of promising to release the special counsel’s final report, which drew concerns from members of both parties.