And he said that, as an American "I'm almost ashamed I haven't produced Williams since I started" at the Old Vic.
The lineup also includes a revival of Terence Rattigan's drama "The Winslow Boy" directed by Lindsay Posner and a British tour of the Old Vic's acclaimed production of Michael Frayn's farce "Noises Off."
Spacey said the lineup reflected the fact that "the Old Vic has always been first and foremost an actors' theater, a home for great talent and memorable performances."
Spacey, who won Academy Awards for "The Usual Suspects" and "American Beauty," has led the Old Vic since 2003.
He has been credited with restoring the fortunes of the 200-year-old venue, which has provided a stage to performers including John Gielgud, Peggy Ashcroft, Alec Guinness, Peter O'Toole, Judi Dench and Maggie Smith.
He has starred in several of its productions, including an acclaimed "Richard III" last year, and has won praise for drawing both broader audiences and stable funding to the venue after years of uncertainty.
Spacey said he would step down in 2015, having helped establish the Old Vic "as a destination theater again."
"I think a theater needs new blood," he said. "I am excited about the transition."