The Hawks sent a 2023 first-round pick via the Charlotte Hornets plus their own 2025 and 2027 first-round picks to the Spurs in the deal. The deal also includes a first-round pick swap in 2026.
The 2025 and 2027 first-round picks are unprotected, a league source told ESPN's Zach Lowe.
The Spurs are expected to waive Gallinari, sources told ESPN's Adrian Wojnarowski.
The Hawks also acquired center Jock Landale in the deal.
The trade gives the Hawks a formidable backcourt with Murray joining All-NBA guard Trae Young. According to Elias Sports Bureau, Murray and Young will be the first pair of teammates in NBA history who each averaged 20 points and 8 assists per game in the previous season.
Murray took to Twitter later Wednesday to express his gratitude to the Spurs.
SAN ANTONIO I LOVE YOU FOREVER.....🖤 Thank You @spurs And The Whole City For Believing In Me And Embracing Me From DAY ONE. I Want To Write A Whole Book But It's Not Easy. We Are Family And Its Always Going To Be Bigger Than Basketball!!! pic.twitter.com/wMrmZanTbj— Dejounte Murray (@DejounteMurray) June 30, 2022
Hawks principal owner Tony Ressler said in May that the team wouldn't repeat the "mistake" of complacency that he believes set the stage for this season's disappointing first-round exit from the playoffs.
The Hawks returned a young core from the team that was eliminated by the Milwaukee Bucks in the Eastern Conference finals two seasons ago. Ressler said he believed the team would improve just based on experience.
"We thought we'd be better this season," Ressler said. "We plan to get better this offseason."
Instead, the Hawks escaped the play-in tournament with the No. 8 seed before losing to the Miami Heat in five games in the opening round of the playoffs.
Murray, 25, averaged a career-best 21.1 points, 9.2 assists, 8.3 rebounds and 2.0 steals in 68 games last season, earning All-Star honors for the first time in his career. He had 13 triple-doubles, setting the single-season franchise record for the Spurs, according to ESPN Stats & Information research.
He is scheduled to make $16.6 million next season and will be an unrestricted free agent in 2024.
Gallinari, 33, averaged 11.7 points, 4.7 rebounds and 1.5 assists in 66 games last season, his second with the Hawks.
Landale, 26, averaged 4.9 points and 2.6 rebounds in 54 games last season, his first in the NBA.
ESPN's Bobby Marks and The Associated Press contributed to this report.