Go to https://www.youtube.com/ in your preferred browser. This will open your YouTube home page if you're logged in. If you aren't logged into YouTube, click Sign in in the top-right corner of the screen and enter your email address (or phone number) and password. This tab is usually on the left side of the YouTube home page. It's on the right side of the page. Doing so removes any previously watched videos from your YouTube history. It's below the Watch history label in the upper-right side of the page. This option is in the same place as the CLEAR ALL WATCH HISTORY option was before. This will clear your search history from your YouTube channel. Your YouTube history is now completely empty.

Summary:
Open YouTube. Click History. Click CLEAR ALL WATCH HISTORY. Click CLEAR WATCH HISTORY when prompted. Click the circular button next to Search history. Click CLEAR ALL SEARCH HISTORY. Click CLEAR SEARCH HISTORY when prompted.