Yes. The way this is done is through your XBOX. Your purchases are tied to your Gamer tag. You can change from one email account, existing account, to another directly on XBOX and all your purchases will transfer. This is in user accounts in settings on your XBOX.
If you are going to be getting a new email address one you don't already own. For example if you want an @outlook.com account you can migrate directly to a new email address on your PC. Just go to your Live account in settings you will see the option to migrate to an outlook account. I did this when I changed to @outlook.com with no issues.