Turner made the announcement during a shareholders' meeting Friday in Atlanta, The Financial Times said.
Turner's company, Turner Broadcasting, was acquired by Time Warner in 1996, which was then taken over by Internet provider AOL in 2001.
The dot-com bust cost the company billions of dollars in stock, and Turner's role in the company has shrunk ever since, the Times said. Despite losing his title as the company's vice chairman, he is still its largest individual stockholder.
The 67-year old Turner plans to focus on his work with the United Nations and his own chain of fast-food restaurants.
Of the last few years, Turner said, "I hung in there as long as I could. I've done my best."
Benedict Cumberbatch's dramatic reading of R. Kelly lyrics is just what you need
Exploding whale video goes viral on Internet