Apple - How can I use an existing Time Machine backup with my new computer?
I found the following solution here:
sudo tmutil associatedisk -a "/Volumes/Macintosh HD" "/Volumes/Time Machine Disk/Backups.backupdb/John Doe's MacBook/Latest/Macintosh HD"
By now, there seems to be a dedicated tmutil command:
sudo tmutil inheritbackup <path to previous time machine backups on mounted volume>
Example:
sudo tmutil inheritbackup /Volumes/Seagate\ Backup\ Plus\ Drive/Backups.backupdb/MacBook
Make sure the name of the new computer's hard drive is the same as the old computer's hard drive. Click once on the hard drive and hit enter to rename.
Make sure the new computer's name is the same as the old computer's name. Open System Preferences, then Sharing. Enter the name in the Computer Name field. (This step may not be necessary, but it's what I did.)
Plug-in the existing Time Machine drive. Open the Time Machine preferences and turn Time Machine on. Click Select Disk… and choose the Time Machine drive. After a few seconds, the backup will start. It will probably take awhile because OS X recognizes that you're backing up an entirely new disk, so backs up the entire disk. It might have to delete a few of your oldest backups, depending on how much space is left on the Time Machine drive.
After the first backup, you can safely change the name of the new computer and its hard drive.
Update: Using this technique, you won't be able to browse any backups from your previous computer with the Time Machine interface (although they are removed when Time Machine needs to free up space for new backups). The old backups are still visible and accessible from the Finder.