My purchased itunes music will not show up on imovie

Apple Music is a subscription service. It's songs cannot be used in iMovie because they are DRM (Digital Rights Management) protected. Downloading them to iTunes will not remove the DRM protection.

To use a song in iMovie you must purchase it directly from the iTunes store without involving Apple Music in the chain of purchase.

-- Rich

That' a good idea.

One last thing to try that's very easy. Go to System Preferences/Security & Privacy/Privacy. In the Privacy window sidebar click on Automation. In the pane to the right scroll the displayed apps until you get to iMovie. Make sure that iTunes is checked under iMovie.

If you are running Catalina, also check in the Privacy window sidebar for an iTunes item. If you find one, click on it and see if you can enable iTunes for iMovie from the pane to the right.

-- Rich

I would try redownloading iMovie.

To update/redownload iMovie 10, drag your iMovie 10 app from the Applications folder into the trash, but do not empty the trash. Sign in to the app store and open your purchases folder by clicking on your name at the bottom of the app store side bar. You will see your purchases displayed, including iMovie 10. Redownload/update iMovie from there. If not successful, drag your present iMovie app out of the trash (if you moved it there) and return it to the Applications folder.

iTunes songs that are in the cloud would not be read by iMovie. However, you said that you had downloaded them so that wouldn't be the problem.

If the redownload of iMovie doesn't work you might consider contacting apple support and talking to the savvy techs there. They have the capability of remotely accessing your computer, that we can't do here. Click on the Contact Support item in the upper right hand corner of this forum's screen and navigate to a place where you can input your telephone number.

If you have time, post back with your results, as it may help others with this problem.

-- Rich