It is now not under File, but in the main menu, goto:
Android Studio -> Preferences -> Appearance & Behavior -> Click on: System Settings -> Then you see: Un-check "Reopen last project on startup" -> Click apply
For Mac users, as of Version 4.1.2, the path is Preferences (CMD + ,) -> Appearance & Behavior -> System Settings -> uncheck Reopen last project on startup.
If you are in a screen of a previous projects:
Customize->All settings-> Appearance & Behaviour--> System Settings --> uncheck Reopen projects on startup(under Project section)