If you only wish to migrate TSM settings, you can open the Backups folder via the TSM Desktop Application and copy the automatically-generated backup files (in .zip format) to your new system or computer in the same directory. From here you can restore the backup through the TSM Desktop Application.

Related article: How do I restore a backup of my addon settings?

If you are aiming to migrate settings for your entire collection of WoW Addons, you can also simply copy your WTF folder within your WoW directory to your new system or computer.