Both sides agreed to a four-year deal, The Athletic's Shams Charania reports.
The 61-year-old replaces Alvin Gentry, who was dismissed in August after five seasons at the helm. Van Gundy's defensive acumen should help a Pelicans squad that surrendered 117.1 points per contest, including an average of 52.2 points in the paint.
Van Gundy last coached in the NBA during the 2017-18 campaign with the Detroit Pistons. He holds a 523-384 career mark across three different clubs in parts of 12 seasons behind the bench.
Van Gundy notably guided the Orlando Magic to four straight 50-win campaigns, including an NBA Finals berth in 2008-09. He worked as a television analyst for TNT during this year's postseason.
"We are delighted to welcome Stan, his wife Kim and their family to the New Orleans Pelicans," Pelicans executive vice president of basketball operations David Griffin said in a statement. "Stan's track record of success as a head coach speaks for itself. His ability to teach while building genuine relationships was one of his many strengths that drew us to him.
"We feel like we are hiring one of the most accomplished leaders and authentic human beings in the NBA."