In the web broswer, I can select all videos from the history and hit the delete button to delete them all. However, if there are more than 100 videos in the history I get an error message. I have to manually select each video individually and then press delete - then keep doing that until there are fewer than 100 left and selecting all and deleting will work.
The other option is to wait 60 days for the videos to go away by themselves but as I log in randomly to see the history I have no idea then which ones I have watched and which I have not.