Carter, 41, will be starting his 21st season in an NBA career during which he has scored 24,868 points.
Atlanta general manager Travis Schlenk wanted Carter's influence around a young, rebuilding roster. Atlanta selected three players, including guard Trae Young, in the first-round of the 2018 NBA draft, and 2017 first-round pick John Collins also is a key part of the franchise's future. Carter was drafted on June 24, 1998, nearly three months before Young was born -- on Sept. 19, 1998.
Carter, an eight-time All-Star, will be joining his eighth NBA team. He averaged 5.4 points for the Sacramento Kings in a limited role last season.
Hamilton, 22, was a second-round pick by the Denver Nuggets in 2016 out of UConn.