How to use the same Time Machine backup when you get a new Mac

If you use Time Machine to backup your current Mac, then get a new Mac, you can continue using the same Time Machine backup.
Part of the first-run setup process on the new Mac is Migration Assistant, a tool built into OS X, asking if you want to restore files and settings from your previous Mac or a Time Machine backup. If you pick the Time Machine backup and allow the process to finish, a dialog will ask if you want the new Mac to “inherit” the Time Machine backup history. If you choose yes, your new Mac will enable Time Machine and continue backing up to your Time Machine archive.

There are a couple things to note here. First, in my testing, the inherit process seems to be an option only when you first setup the new Mac. I just tried it now with Migration Assistant (Applications > Utilities > Migration Assistant) on this new Mac I’ve been using for a couple of weeks, and I wasn’t given the option to inherit the backup.

Finally, if you tell the new Mac to inherit your Time Machine backup, your old Mac will no longer be able to use that backup for Time Machine. It will have to start a new archive.