Wright plans to remain on the job for a few weeks during a search for his successor, an executive familiar with his plans who asked not to be identified said late Thursday.
He is the second high-ranking Turner programming executive to leave this year. In April, Steve Koonin, the head of Turner Entertainment Networks, left the company to become chief executive of the Atlanta Hawks professional basketball team.
Wright has been with Turner more than a decade. He is credited with being a key member of the programming team that put TNT and TBS on the map with such popular and critically acclaimed original dramas as "The Closer," "Falling Skies" and "Men of a Certain Age."
He helped woo late night comedian Conan O'Brien to TBS after O'Brien's high-profile exit from NBC.
The departures of Wright and Koonin underscore management turmoil at Turner, which accelerated when longtime Turner Chief Executive Phil Kent retired at the end of last year.
Former ad sales chief David Levy was installed as president of Turner Broadcasting System last summer. He promptly introduced to the organization a new management style.
While Wright had applied for Koonin's job, and was said to be in the running, his chances probably were diminished earlier this year after Jeff Bewkes, CEO of parent company Time Warner, expressed disappointment in TNT's programming.
During a call with Wall Street analysts, Bewkes acknowledged that the Turner channels "didn't take enough creative risks."
Koonin's job also is vacant. The company has been interviewing candidates this summer.
TNT has suffered during the last year from sagging ratings. Some of its highest-rated shows appeal to an older audience that is outside the target of advertisers who pay a premium to reach younger viewers.
However, TNT has turned in a particularly strong performance this summer with several top-rated cable shows. The list includes "Rizzoli & Isles," "Major Crimes" and the Michael Bay drama "The Last Ship."
Earlier this week, Turner CEO John Martin unveiled broad cost-cutting for Atlanta based Turner Broadcasting. The company immediately offered buyouts to nearly 600 older workers who have been with the company at least 10 years.
Martin became CEO at the beginning of the year.
Turner employs about 9,000 workers in the U.S.
Hollywood news site Deadline first reported Wright's planned exit.