How do I insert an already uploaded video file into my Media Library?

I’m having problems with the WP uploader (hosting issue); WP is pooping out after uploading files that are relatively large (> 32MB).

My idea was to upload the video file via SFTP to the server and then try to get WP to insert it into the Media Library. How do I do this?

I know that it isn’t as simple as just putting it into wp-content/uploads/<date-path>/ because there is some meta-data to add to the back-end DB.

I’ve seen some posts for media_sideload_image but looking at the code, it looks like this is specifically for images. I looked at media_handle_sideload but I’m not sure how it works or how to create a solution to insert this file where it needs to go. For example, the comments say:

@param array $file_array Array similar to a {@link $_FILES} upload array

What does {@link $_FILES} upload array mean?