I purchased CBS All Access on my iPhone/iPad. Can I use the same subscription on my Apple TV?

Yes! Launch the CBS app on your Apple TV, and then:

Apple TV 3rd generation or earlier

1. From the homescreen, select any subscriber-only show. 
2. You'll be presented with a Sign Up/Sign In screen. Select "Purchased through iTunes? Restore." at the bottom of the screen.

1. From the homescreen, select "Settings" and "Sign In." 
2. Select "iTunes Subscriber? Restore."