As questions swirl about his credibility, former Trump campaign adviser Roger Stone settled a defamation suit seeking $100 million in damages on Monday for publishing false and misleading statements on InfoWars.com, a far-right website known for promoting conspiracy theories.

The agreement requires Mr. Stone to run ads in national newspapers, including The Wall Street Journal, apologizing for making defamatory statements about a Chinese businessman who is a vocal critic of Beijing. It also requires Mr. Stone to publish a retraction...