Terms of the deals were not disclosed by the club.
Humphries, 31, averaged 6.4 points and 3.4 rebounds in 21 games with the Hawks last season. The 12-year veteran recorded 6.5 points and 4.1 rebounds in 53 contests with Washington, Phoenix and Atlanta in 2015-16.
"We're thrilled to be able to bring Kris back to Atlanta," Hawks president of basketball operations and coach Mike Budenholzer said. "He quickly fit in with our team last season and played an important role on the court and in the locker room."
A former Georgia Tech standout, Jack averaged 11.1 points and 4.5 assists in 803 contests over his 11-year career. The 32-year-old ratcheted it up a notch last season with Brooklyn, recording 12.8 points and 7.4 assists in 32 games.
"Jarrett brings a wealth of knowledge and experience to our backcourt," Budenholzer said. "His leadership and versatility will be important to our team."
Delaney averaged 14.6 points and 4.9 assists last season for the Russian team Lokomotiv Kuban.