Teletovic tweeted a picture of himself in a Suns jersey and added in another tweet: "Thank you Brooklyn Nets and Nets fans for 3 great years!!!"
He is signing a one-year, $5.5 million contract with Phoenix, sources confirmed to ESPN.com.
Teletovic's announcement came shortly after the Nets rescinded their $4.2 million qualifying offer, making him an unrestricted free agent.
Teletovic, 29, missed significant time last season after being diagnosed with multiple blood clots in his lungs.
In three seasons, he owns career averages of 7.0 points and 3.4 rebounds per game. A 6-foot-9 floor spacer, Teletovic is a career 36.2 percent shooter from 3-point range.