Spellman, the 30th pick in the 2018 draft, appeared in only 46 games for the Hawks last season, averaging 5.9 points and 4.2 rebounds in 17.5 minutes per game before his season ended with an injury.
Spellman plays center, where he will join a rotation that includes Kevon Looney, Willie Cauley-Stein and Alen Smailagic, and power forward, where he would be paired with former Villanova teammate Eric Paschall behind Draymond Green.
The trade also represents a payroll savings for the Warriors, as Jones is scheduled to make $2.3 million next season and Spellman $1.9 million.
Spellman acknowledged in January that one reason he did not see much time for the Hawks early on was his weight.
"Pretty much, I was fat," Spellman said. "I had to lose weight. That's what allowed me to get back."
Spellman spent some time in the G League and returned slimmer, but his season ended on March 1 when he suffered a high left ankle sprain.
Jones appeared in only 25 games for the Warriors over his first two years. Last season, he was promoted and started 22 games at center before suffering a torn pectoral muscle. He briefly returned at the end of the playoffs.
Over three seasons, Jones averaged 3.6 points and 2.3 rebounds per game and won two rings.