The film, which follows the tense relationship between Laurence Olivier and Monroe during the production of The Prince and the Showgirl, has started production in the UK for a seven-week shoot.
Williams will be joined by Eddie Redmayne, Kenneth Branagh, Judi Dench, Dominic Cooper, Emma Watson, Julie Ormand and Dougray Scott in the cast for director Simon Curtis's biopic.
Redmayne is playing Monroe's assistant Colin Clark, while famous figures such as Olivier (Branagh), Monroe's husband Arthur Miller (Scott), actress Vivien Leigh (Ormond) and Dame Sybil Thorndike (Dench) also figure in the story.
Zoe Wanamaker, Toby Jones, Philip Jackson, Geraldine Somerville, Derek Jacobi and Simon Russell Beale round out the cast.
BBC Films and The Weinsten Company are teaming up to finance the project, to be produced by David Parfitt.
"We are truly thrilled to be working with the immensely talented Simon Curtis on his feature debut, with our trusted partners and good friends producer David Parfitt, Christine Langan and BBC Films, from a remarkable true story, beautifully realised script, stellar cast and top-notch crew, we couldn’t be happier embarking on this production," said Weinstein Company co-chairman Harvey Weinstein in a statement.