You can turn your personal account into an organization by going to Account Settings > Organizations, clicking "Turn into an organization", and following the instructions in the pop up dialog.
The history of the account and the repositories will be preserved.
I'll explain each point of the warning you'll get:
You will no longer be able to log into YOURACCOUNT (all administrative privileges will be bestowed upon the organization owners you choose)
This just means that you need to choose a new personal account(s) to add as the owner(s) of your new organization. You need to do that anyway, because you can't log in as an organization. You need to create at least one new personal account for you.