Those are just backups of your original files that
gedit creates before saving changes to your edited documents.
gedit preferences you need to disable Create a backup copy of file before saving, and if you want to automatic save your edits automatically set a timer with the option enable Autosave files every X minutes.
That way the
~ will be gone and your last changes will be saved on the file every x minutes in case something goes bad or your computer crashes.
The changes made to the file will be saved to the file itself and not to a temporary file.
Please be aware that if you delete the contents of a file and auto save is enable there will be a chance that you end up with a saved empty file.
Always make sure that when you close on file while auto save is enabled that the contents of the file are correct, else undo them and save the file again.