Following the private cremation relatives including his widow Donna Wilson Scott and film maker brother Ridley Scott announced the foundation of a scholarship at the American Film Institute to honour his creative legacy.
In a statement to The Hollywood Reporter, they said: "The family ask that in lieu of flowers, donations be made to the fund to help encourage and engage future generations."
The Top Gun filmmaker jumped from a bridge into Los Angeles Harbour on August 19.
The last film the 68-year-old Brit directed was 2010's Unstoppable. He is survived by Donna, whom he married in 1994 and their twin sons Frank and Max, who were born in 2000.