How do I authorize my Mac to download previous purchases on Apple TV?

I’m having trouble watching a movie on Apple TV that I just bought on my Mac. It says, “You need to authorize this computer in the Account menu before you can download previous purchases.” I’ve never experienced this before, and I tried Googling for a solution, but I couldn’t find anything. I think I may have made it worse by removing my Mac from the system, and now I can’t find the option I used to remove it. I know this is a bit confusing, but I hope someone can help a hopeless IT guy out.

[Re-Titled by Moderator]

Original Title: You need to authorize this computer in the Account menu before you can download previous purchases