Since Blogger (blogspot) isn't an actual hosting company, there's no real way to transfer the site from Blogger to your account with us directly.

However, Blogger has a feature which will allow you to export your site content to a more universal format.

They have a FAQ entry on how to accomplish it here.

WordPress does support importing directly from your blogger account:

Simply install WordPress from MOJO Marketplace in your cPanel.

Then in your WordPress Admin area (example.com/wp-admin), go to Manage → Import → Blogger and follow the directions to complete the import.