Carter will sign with the Milwaukee Bucks once he clears waivers, according to his agents.
Carter was let go by the Nets on Monday after they reached an agreement with Dragic. Carter is the second perimeter player this month to choose the Bucks after being cut by the Nets.
The loss of Donte DiVincenzo, who was traded to the Sacramento Kings, and Pat Connaughton, who is out for a month due to hand surgery, has impacted the depth of the backcourt.
Steve Nash was Dragic's former teammate and the reason why the Bucks lost out on him.
Carter joined the Nets in an off-season trade with the Phoenix Suns and averaged 3.6 points in 46 games. Carter was drafted 32nd overall by the Memphis Grizzlies in the NBA draft.