The papers include photos, drawings and correspondence with theatre giants including Samuel Beckett, Laurence Olivier and Tennessee Williams.
The director worked with Olivier in several RSC productions.
Brook, 89, said he was delighted the papers "which preserve something of the most ephemeral of art forms, will be made available to future generations".
The V&A acquired Brook's archive with support from the Heritage Lottery Fund (HLF) and a private dono"
