As Google works to transition its users from Google Play Music to YouTube Music, one crucial aspect is importing libraries. A recent story from Droid Life reports that the ability to transfer your content is now available, at least for some users. You can check if it's available on your account through this link: music.youtube.com/transfer. You'll just need to click on a single button at the bottom of the screen to start the process.
The capability should be available on the YouTube Music app, but it doesn't seem to be available there for some users. They tried using the web portal (which we linked to above) and got it to work. Google appears to be rolling this feature in waves, so if you don't have it yet, keep checking in.