The final season of the critically-acclaimed show, which is due for release in autumn, is expected to cover events from 1997 to 2005, and show the early relationship between Prince William and Kate Middleton – now the Prince and Princess of Wales.
Green, 26, will star as fourth-year law student Rupert Finch, who dated Kate at St Andrews University for a year before she got into a relationship with Prince William.
A series of stills from the filming of The Crown were released earlier this year showing Ed McVey as William, Meg Bellamy as Kate, and Oli as Rupert.
One shows Rupert and Kate holding hands as they walk around the streets of St Andrews in Scotland.
Green is an alumni of the Strasberg Theatre & Film Institute in New York. He has previously starred in The Bold and the Beautiful, The Mosquito Coast and A Good Person.
Green is dating Layer Cake star Miller - who recently confirmed she was expecting her second child with her boyfriend.
The couple made their relationship red-carpet official at a Vanity Fair party in February 2022.
Miller debuted her growing baby bump during a trip to the beach in Ibiza on Monday.
Miller, who is also known for appearing in 21 Bridges, is already mother to daughter Marlowe, 10, who she shares with her ex Tom Sturridge.