Hampton will receive a Minor League contract with an invite to Spring Training.
In other news, the D-backs have strong interest in veteran backup catcher Henry Blanco, but a baseball source said a deal at the moment was "not close."
Hampton was signed by the D-backs last August, and in 10 games down the stretch for them, Hampton did not allow a run in 4 1/3 innings.
D-backs GM Kevin Towers told reporters Tuesday that he expected to hear back from Hampton on the team's offer to him Wednesday.
Towers has remade the bullpen in recent weeks, but the one thing he was still looking to add was a left-hander.