She will play the title character based on a real-life woman who set up home in a battered van on the writer's north London driveway for many years.
The film will be directed by outgoing National Theatre boss Nicholas Hytner and star Alex Jennings as Bennett.
It is part of a string of new films announced by the BBC ahead of this year's Cannes Film Festival in the south of France.
Others include City of Tiny Lights with Riz Ahmed playing London private eye Tommy Akhtar, and Pride, a comedy drama with Dominic West and Sherlock star Andrew Scott about a group of gay activists who support striking miners in 1984.
BBC Films boss Christine Langan said: "Our ambition is to be a creative hub enabling exciting British filmmakers to tell their stories. From Pride at Cannes through to today announcing The Lady in The Van with Alan Bennett, BBC Films nurtures a comprehensive range of films from inception, through production, cinema release and to their eventual home on BBC Two."
Other projects include Dame Helen Mirren starring in Woman in Gold based on the real-life story of a Jewish survivor of the Second World War who fought a legal battle to reclaim several paintings by Gustav Klimt that were stolen from her family and Sir Ian McKellen who will play an ageing Sherlock Holmes in A Slight Trick of The Mind.