The Top Gun helmer died on August 19 after jumping off the Vincent Thomas Bridge in Los Angeles.
A scholarship fund has now been set up by Scott's family at the American Film Institute (AFI).
The AFI is a national arts organisation founded in 1967 to preserve the legacy of American film and nurture upcoming American film-making talent.
In a statement to The Hollywood Reporter, the Scott family asked that "in lieu of flowers, donations be made to the fund to help encourage and engage future generations of film-makers".
As a popular and successful figure, Scott's sudden death has shocked the Hollywood community. His funeral, a private ceremony for family, took place this weekend.
Watch a fan-made tribute to the movies of Tony Scott below:
