Rehearsals for the production will begin early-mid 2011, according to a casting notice.
EW.com had previously reported that Billy Crudup, who originated the role of Septimus Hodge in the play's 1995 Broadway debut, will play the role of Bernard Nightingale in the revival.
No official announcement about the production has been made.
Leveaux received Tony nominations for his direction of Jumpers, Nine, The Real Thing, Anna Christie and A Moon for the Misbegotten.
Tom Stoppard's 1993 play Arcadia premiered at the National's Lyttelton Theatre in 1993 before transferring to the West End's Theatre Royal, Haymarket, and was subsequently presented at Broadway's Vivian Beaumont Theater under the auspices of Lincoln Center Theater in 1995. Both the original West End and Broadway productions were directed by Trevor Nunn, and the play won both the Laurence Olivier Award and New York Drama Critics' Best New Play Award.
In publicity materials for the 2009 London revival, the play is described as "a dazzling, witty masterpiece of misunderstanding and quest for knowledge, resonating across centuries." The play is set in two time periods: in April 1809, at a stately home in Derbyshire, a gifted pupil called Thomasina proposes a startling theory, beyond her comprehension. All around her, the adults, including her tutor Septimus, are preoccupied with secret desires, illicit passions and professional rivalries. Two hundred years later, academic adversaries Hannah and Bernard are piecing together puzzling clues, curiously recalling those events of 1809, in their quest for an increasingly elusive truth.