CleanExit

Clear browsing data when Edge is closed and reopened, giving you a fresh, private browsing experience. Removes: ✓ Browsing history ✓ Download history ✓ Cookies and other site data ✓ Cached images and files ✓ Passwords and other sign-in data ✓ Autofill form data ✓ Hosted app data Simply select the data types you want removed in the extension pop-up, and the data will be deleted the next time Edge is closed and re-opened. Source code is available at the link provided.

Screenshots from Chrome Web Store

Screenshots from Edge Add-ons