Covent Garden Music Director Antonio Pappano will conduct and Richard Jones will direct, the company announced Wednesday.
Turnage is the composer of "Greek" and the West End show "Jerry Springer: The Opera." The libretto is by Richard Thomas.
Smith died of an accidental drug overdose in 2007. She was 39.
She was Playboy's Playmate of the Year in 1993. She married 89-year-old J. Howard Marshall II the following year. After his death in 1995, she fought a protracted legal battle with his son over his estimated $500 million fortune.
Smith died five months after the death of her 20-year-old son from her first marriage. Daniel Smith died of an accidental overdose in the Bahamas hospital room where his mother had days earlier given birth to a daughter.
The company also said the world premiere of Judith Weir's "Miss Fortune," a co-commission with the Bregenz Festival, will take place in Bregenz on July 21, 2011. The production will open the Covent Garden in March 2012 as part of the buildup to the London Olympics that summer. The opera is based on a Sicilian folk talk about a woman whose wealthy family has hit hard times.
The Royal Opera's 2010-11 season also will include the British premiere of Steffani's "Niobe" (opening Sept. 23 in a production seen at the 2008 Schwetzingen Festival), and new productions of Cilea's "Adriana Lecouvreur" (November starring Angela Gheorghiu and Jonas Kaufmann); Wagner's "Tannhauser" (Dec. 11 starring Johan Botha and Westbroek); Rimsky-Korsakov's "The Tsar's Bride" (April 2011 starring Marina Poplavskaya); and Massanet's "Cendrillon" (July 2011 starring Alice Coote and Joyce DiDonato).