Created by Steven Knight, the hit BBC drama stars Cillian Murphy as the leader of the Peaky Blinders gang in 1920s Birmingham, England.
"From Steven Knight's writing to the consistently brilliant production, I couldn't feel more privileged to be invited to join this iconic show," Sam said in a statement, while Anya added: "I could not possibly be more excited to be joining such a talented group of people. I can't wait to get in and play this character."
The actress shared a picture of herself dressed in character on Instagram and added, "Welcome to Birmingham... Let's play," complete with ticking bomb emojis. It is not known what roles her and Sam will play.
They will be joined by Brian Gleeson, the brother of Domhnall and son of Brendan Gleeson, who said: "Looking forward to kicking around in the mud of Northern England with an exceptional cast and crew. The scripts are wild and pertinent - a classic Peaky brew."
Other newcomers include "Humans" actor Neil Maskell, Anya's "The Witch" co-star Kate Dickie and "Lady Macbeth"'s Cosmo Jarvis, as well as Emmett J Scanlan, Elliot Cowan, Charlene McKenna, Andrew Koji, and Daryl McCormack.
Season five of the BAFTA Award-winning show is currently filming ahead of a 2019 broadcast on BBC One. According to the BBC, the upcoming season will be set after the financial crash of 1929. It follows Tommy, now a member of Parliament (MP), as he is approached by a charismatic politician with a bold vision for Britain and realises that his response will affect the entire nation, not just his family.
The series is being directed by Anthony Byrne and feature returning cast members Helen McCrory, Paul Anderson, Sophie Rundle, Finn Cole, and Aidan Gillen.