First reported by +Nedas Petravičius, the button will be found in a prominent place on the YouTube Upload page under a "Import videos" header with a large Google+ logo. You can't miss it.
When pressed, you'll be greeted with the usual Google+ filters to select from: All videos, Auto Backup or Albums. Multiple can be selected and uploaded at a time, and goes through the usual steps (options to add title, description and tags etc) like when you upload a video the standard way.
The update is in the later stages of rolling out, and should be available to most people by now but if not, check back in a day or two.
So readers, will you be making use of the new Google+ video import tool?