Major served as Prime Minister of the UK and leader of the Conservative Party from 1990 to 1997, the year Princess Diana died.
Major is now 78.
Miller became famous for his role in “Trainspotting,” and has acted in “EastEnders” and “Prime Suspect.” He has also played Sherlock Holmes in “Elementary.”
Production on the new season of the Netflix hit is expected to start this summer. Elizabeth Debicki will play Princess Diana, Dominic West will play Prince Charles, Imelda Staunton will play Queen Elizabeth, Jonathan Pryce will be Prince Philip and Lesley Manville will play Princess Margaret.
The new season will cover the royal family in the early 1990s.