DuPont said the change in ownership will not affect ticket holders for 2014-15. The spring season includes performances of "Camelot" and "Guys and Dolls."
In September, Trian Fund Management, an activist fund headed by Nelson Peltz, cited the theater, along with DuPont's ownership of a hotel and country club, as examples of "excessive" costs, in a letter calling for the DuPont to be broken up into three companies.
On Thursday, Trian restated the demand and nominated Peltz and three others to the DuPont board.
Trian said it took the action because of board resistance to its efforts to improve DuPont's "flawed business plan." Trian owns about 3% of DuPont shares.
DuPont built the theater and the other hospitality assets to attract employees.
The theater was once a stopping point for shows before opening on Broadway in New York.
However, the attractiveness of the Delaware house to production companies has diminished due to its capacity of less than 1,300 seats, said a report in the Wilmington News Journal newspaper.
Copyright Agence France-Presse, 2015