Attorney General Jeff Sessions appointed Geoffrey Berman, a law partner of White House ally and former New York Mayor Rudy Giuliani, to be the temporary U.S. Attorney in Manhattan, the Justice Department said Wednesday.

The announcement included 16 other interim top prosecutors for districts around the country, and followed a lengthy process to nominate new U.S. Attorneys. In March 2017, Mr. Sessions asked all of those previously appointed by former President Barack Obamato resign, but the White House has yet to nominate permanent...