Richardson, 29, averaged 11.5 points in 42 games for the Spurs this season. He provides the Pelicans with depth on the wing and future salary-cap flexibility by removing Graham's $12.1 million from their books for the 2023-24 season.
San Antonio, meanwhile, continues to add to an ever-growing pile of draft picks it has accrued over the past several months, including a protected first-round pick and two second-rounders the Spurs received for Jakob Poeltl early Thursday morning.
Graham averaged 5.3 points in 53 games this season for New Orleans.
The Athletic first reported the Spurs-Pelicans trade.