WASHINGTON—A House panel formalized procedures for its investigation into whether to recommend articles of impeachment against President Trump, advancing a long-running probe but offering little clarity on Democrats’ end game.

The resolution, which the House Judiciary Committee passed along party lines Thursday, authorizes Chairman Jerrold Nadler of New York to designate certain hearings as part of the continuing investigation. It also gives committee lawyers the chance to question witnesses for an hour after all lawmakers...