Here at Microsoft's Ignite 2019 conference, the company announced the general availability date for its new Chromium-based Edge browser. The rebuilt Edge will be available on January 15. In fact, if you sign up for the Beta channel, you can get the release candidate right now.
The next question is that of when the browser will actually ship with Windows 10, with many speculating that it might ship in 20H1 - which would be the first feature update after January 15 - or even 20H2, since 20H1 might RTM in December. As it turns out, neither of those theories are accurate, as the browser will start to be bundled with the OS right after the GA date.
It's going to be a slow rollout though. We're not all going to wake up one day and find Legacy Edge replaced by the new Edge. That's how staged rollouts work though. There will be a small sample group that will get it first, and then that group will be expanded. As for new installations of Windows, the bits will be sent out to OEMs as soon as they're generally available.
The point is that it doesn't require a Windows 10 feature update at all. The app can simply be bundled with the OS, and as we've seen, when Edge is installed from the production branch, it replaces Legacy Edge, or Edge Spartan. So if you buy a new PC next year, chances are that it will be running Edge Chromium out of the box.