Vita and Virginia is based on a play of the same name by Eileen Atkins, which debuted in 1992.
The Hollywood Reporter confirms that Green has been signed up to play Woolf, a literary icon, whilst Arterton will play author Sackville-West.
Woolf, nee Stephen, married Leonard Woolf in 1912 and met Sackville-West – wife of Harold Nicolson – in 1922.
They began a sexual relationship that lasted nearly a decade, and is spoken of in their various letters and diaries.
Green, who shot to prominence in the James Bond movie Casino Royale in 2007, has been keeping busy in recent years with work such as Miss Peregrine’s Home for Peculiar Children and Dark Shadows.
She also starred in Penny Dreadful, which came to an end in 2016 after two years on-air.
Arterton, meanwhile, has also graced the world of 007, having starred in Quantum of Solace as Strawberry Fields in 2008.
She’s also popped up in Gemma Bovery, Hansel & Gretel: Witch Hunters and Tamara Drewe; additionally racking up acclaim for stage work in Made In Dagenham and Nell Gwynne.
Virginia Woolf, who died in 1941, is responsible for works including Mrs Dalloway, To The Lighthouse and Orlando – the latter of which was inspired by the family history of Sackville-West.
The latter writer died in 1962 at the age of 70.