AT&T Inc. said it is shaking up its WarnerMedia unit, doing away with an outdated structure in a bid to make the company more competitive in an entertainment industry reshaped by consolidation and technology.

The reorganization announced Monday breaks up the company’s Turner unit, whose parts will be absorbed by other divisions. In another significant move, a programming czar has been put in place to guide the creative operations at HBO, Turner and a new streaming service WarnerMedia is launching later this year.

Former...