How to Turn Off History in Mozilla Firefox Browser? Open the Firefox Browser. Select the “Tools” Drop-down Menu from the Top of the Window. Select “Options” and Choose “Privacy.” Click the “Firefox Will” Drop-down box and Select “Use Custom Settings for History.” Uncheck the “Remember my Browsing and Download History” Option. Also Uncheck the “Remember Search and Form History” Option. Click “OK” to Save Your Settings. This is How You Turn Off History in Mozilla Firefox.