The funds will be used to help the Royal Dramatic Theater in Stockholm set up an international theater festival in Bergman's honor and buy the rights for scripts to his stage performances.
It will also enable new copies to be made of his films, Prime Minister Fredrik Reinfeldt said in a joint statement with Culture Minister Lena Adelsohn Liljeroth.
"Bergman has given Swedish stage art a unique position in the world. It deserves to be recognized both for a Swedish and international audience," Reinfeldt and Liljeroth said in the statement published in Stockholm newspaper Dagens Nyheter.
The famed director died July 30 at age 89 in his home on the Baltic Sea islet of Faro.
One of great masters of 20th century cinema, Bergman won numerous international awards, including Oscars for best foreign film for "The Virgin Spring," "Through a Glass Darkly" and "Fanny and Alexander."