The Justice Department and Federal Communications Commission have nearly wrapped up their reviews of AT&T Inc.’s $49 billion acquisition of DirecTV and aren’t likely to block what would be the biggest media deal of the past year, people familiar with the matter said.

The posture contrasts with the strong opposition from the agencies that killed Comcast Corp.’s $45 billion deal for Time Warner Cable. It also comes despite warnings from companies like Netflix that a combined AT&T and DirecTV would have the ability and...