Altman, 80, will direct "Resurrection Blues," the play Arthur Miller was reworking on at the time of his death, Spacey announced during the season's media day Thursday.
Spacey said the combination of Altman -- director of "M*A*S*H" and "Gosford Park" -- and Miller was "a double whammy" for the theater.
Spacey, preparing to star in "Richard II," said he will return next fall to star in Eugene O'Neill's "A Moon for the Misbegotten."
Between "Richard II" and "Resurrection Blues," Ian McKellen will return as Widow Twankey in the Christmas pantomime "Aladdin," Spacey said.
The Old Vic will then be the site for a production of Igor Stravinsky's "The Soldier's Tale," performed by a combination of British and Iraqi actors.