According to reports in the Daily Mail, the production will play a limited season in London following the success of its Broadway run which finished earlier this year.
Off-Broadway, the show played 1,195 performances at the John Houseman Theatre from 1987 to 1990 and was adapted into an Oscar-winning film in 1989 starring Jessica Tandy and Morgan Freeman.
The play's Broadway revival starring Redgrave and Jones opened at the Golden Theatre on 25 October 2010, running through to 9 April 2011.
Driving Miss Daisy sees a widowed Jewish woman deemed too old to drive by her son, who hires an African American man to serve as her chauffeur. Set against the backdrop of the mid-century civil rights struggle, what begins as a troubled and hostile pairing blossoms into a life-altering friendship.
Vanessa Redgrave's last London stage outing was The Year of Magical Thinking, the National Theatre's staging of Joan Didion's memoir, directed by David Hare. The one-woman play transferred to the NT Lyttelton in 2008 following a 2007 Broadway run.
James Earl Jones was last seen in the West End last year as Big Daddy in an all-African-American production of Tennessee Williams' Cat on a Hot Tin Roof. The Whatsonstage.com Award-winning production opened in December 2009 at the Novello Theatre following a New York run at the Broadhurst Theatre.
Further London casting for the production is still to be announced.