The 6-foot-5 combo guard is signing a three-year, $29-million deal with the Mavericks, his agent told Wojnarowski.
Dallas will send Memphis two second-round picks in the trade.
Wright flourished following his midseason acquisition from the Toronto Raptors, averaging 12.2 points, 5.4 boards, and 5.3 assists per contest across 26 appearances.
The 27-year-old has developed into an adequate defender with his length and should start alongside phenom Luka Doncic in Dallas' backcourt.
Wright's departure means second overall pick Ja Morant will likely take the reins at the point for Memphis.
The Mavericks were reportedly expected to give Wright an offer sheet. The sign-and-trade allows the Grizzlies to recoup some assets for the former first-round pick.
Memphis will also create a trade exception worth half of the outgoing salary for Wright, according to ESPN's Bobby Marks.