Thurman is best known for her roles in the movies "Dangerous Liaisons," "Pulp Fiction" and "Kill Bill."
British film star Tom Wilkinson and Welsh actor Rhys Ifans are also to star as father and son in another TV version of a stage drama, Caryl Churchill's "A Number."
The movies are co-productions of the BBC and the U.S. cable television network HBO. They are expected to air this year, the BBC said.
"The single play is an integral part of the overall BBC drama picture," said Jane Tranter, controller of BBC Fiction. "We're delighted that this year plays from David Hare and Caryl Churchill, two of the U.K.'s most prolific and significant playwrights, have found their home on BBC Two."