The "Get Out" director will executive produce the series under his Monkeypaw Productions company.
He will also take over narrating duties from creator Rod Serling, who was featured on the original series from 1959 to 1964.
"Rod Serling was an uncompromising visionary who not only shed light on social issues of his time, but prophesied issues of ours," Peele says. "I'm honoured to carry on his legacy to a new generation of audiences as the gatekeeper of 'The Twilight Zone'."
The show will begin production in the autumn and premiere on U.S. network CBS All Access next year (19).