The deal is worth $47 million over four years.
New Orleans is sending Charlotte its 2022 lottery-protected first-round pick, sources said.
Graham, 26, had a breakout season with the Hornets in 2018-19, averaging 18.2 points and 7.5 assists in 63 games. He finished fifth in the NBA's Most Improved Player voting -- an award won by his new teammate Brandon Ingram.
After the Hornets drafted Ball, Graham was used in a variety of different ways -- sometimes starting with Rozier and Ball, other times coming off the bench late in the season -- but his production slightly dipped to 14.8 points and 5.4 assists per game.
Graham's never shot higher than 40% from the field in any season, but he has been a steady 3-point shooter the past two seasons at 37.3% in 2019-20 and 37.55 last season. His 218 makes from deep two seasons ago ranked fifth in the NBA.
According to Second Spectrum, Graham shot 42.6% on catch-and-shoot 3-pointers last season, a mark that was ninth out of 62 NBA players who shot at least four catch-and-shoot 3-pointers a game.
Graham went from 210 catch-and-shoot 3s two years ago to 296 last season, shifting more as the Hornets played with LaMelo Ball controlling the show.