PHPStorm: Disable Auto Opening of File transfer tool window

Open Tools > Deployment > Options and change Operations logging to "Errors only".

If you change the View Mode to Undock and drag the inner edge of the File Transfer window outside the viewport, it will effectively be disabled. This is not very elegant and I hope JetBrains gives us a setting to disable this soon.

To see the File Transfer window again, right-click on File Transfer and select another view option such as Dock Pinned.

As of PHPStorm 2019.1.2. Thanks to Erenor's comment for the inspiration.

Edit: Ástþór's answer does work provided none of the transfers are throwing errors. Due to the way a server is set up on one of my projects, it always gives a benign error, which makes the File Transfer window pop up.

There is no such option in Settings/Preferences.

Just close the window (minimize it) and it will not show up again for this session (only notifications, which you can disable if so desired via Settings/Preferences | Appearance & Behavior | Notifications -- look for "Web deployment" entries).