Inherit Time Machine backup after changing source hard drives
When you plug in the new HDD, do you get a message saying


  Would you like this computer to inherit the backup history from xxx on the "xxx" backup disk?" 


then an option to choose 


  Don't Back Up Now, Create New Backup or Inherit Backup History? 


If so, click Inherit Backup History. If not, follow the steps below:
Open Finder and navigate to your backup location

In terminal, type (but do not press return yet

sudo tmutil inheritbackup


Drag the backup location to the end of the terminal command, and press return for Terminal to navigate to the correct path.

If it was successful, it will ask you for your password. (It won't be shown in the Terminal window as you type.) 

An alternate method would be to "Associate the OS X volume, which is:

sudo tmutil associatedisk -a /


You will drag (from the Backups.backupdb folder) the folder containing the backups from the old drive into the Terminal window for the path. Again, if prompted, enter the Admin password.