The reboot will be produced by CBS Television Studios, which made the original series, along with Peele's Monkeypaw banner. Marco Ramirez (Marvel's The Defenders, Sons of Anarchy) has been hired to write and will be the showrunner.
So far, CBS has had success with using CBS All Access as ground to launch continuations of Star Trek and The Good Wife. The streaming service is home to Star Trek: Discovery and The Good Fight. Other upcoming shows for the service include Strange Angel, $1 and No Activity.
CBS has been talking about rebooting The Twilight Zone frequently. In April 2016, The Wrap reported that CBS was teaming up with Interlude and BioShock creator Ken Levine to create an "interactive" new Twilight Zone. However, that project never came to be. Levine said at a March 2017 Q&A that it was "in flux."
In June, Variety reported that a movie was in the works with Christine Lavaf writing for Warner Bros. That project hasn't taken shape yet either.
The Twilight Zone was a science fiction anthology series created by Rod Serling, who served as narrator. The original series ran from 1959 to 1964, with revivals in the 1980s and early 2000s. John Landis also oversaw the 1983 Twilight Zone anthology movie.