The American actor is joining the all-new cast of the series, which tells the story of the royal family over the course of decades.
"I am so excited to be joining the cast and crew of The Crown and to have the opportunity to portray such a complicated and controversial woman," Anderson said. "Thatcher was undoubtedly formidable but I am relishing exploring beneath the surface and, dare I say, falling in love with the icon who, whether loved or despised, defined an era."
The third season of the series debuts a whole new cast of actors -- Olivia Colman as Queen Elizabeth II, Tobias Menzies as Prince Philip, Helena Bonham Carter as Princess Margaret and Ben Daniels as Lord Snowdon. They replace actors who played younger versions of the same characters in Seasons 1 and 2 -- Claire Foy, Matt Smith, Vanessa Kirby and Matthew Goode.
Season 3 begins in 1964 and will cover such events as the rise of the Beatles and England winning the 1966 World Cup.
The third season debuts Nov. 17.