Question

I know that there’s a “Change Disk…” button in Time Machine, but what if you want to migrate the data (hours, weeks, and maybe even months) to a new, larger disk without starting over again?

Answer

I recently had to migrate all my TM backups to a larger drive.

You can successfully complete the operation using to the following tutorials:

• How To Move OS X Time Machine Backups To A New Disk
• A Bigger Time Machine without Changing History

Check more discussion of this question.