Yes Microsoft has a page that is very clear about the criteria. You have to run the upgrade from an existing Windows installation and if you are already running Windows 8 you need to install the updates to get the Upgrade offer (1, 2).
If you experience issues on a machine or license eligible for the upgrade to Windows 10 and you don't want to look up and interpret how the error codes relate to your situation you can take the shortcut and reinstall from Windows 8 refresh media after you have made a backup of your installation. (I prefer dism/imagex for backups.)
I just found this out while trying to get my upgrade, having a few error codes, tried cleaning and re-downloading a few times and found a suggestion to just install from the Windows 10 refresh media, which are already available, but this doesn't work for the upgrade of an existing license. However since I had a backup and nothing to loose I gave Windows 8 refresh media a chance and was surprised that at the end right before it would bring me to the Windows 8 desktop it notified me about the Windows 10 upgrade as part of the Windows 8 installer and started downloading and installing Windows 10 after I confirmed that this is what I want and not to skip this instead. The installation just finished and Windows 10 activated on the second try.
I would have expected a requirement to download and install all updates for Windows 8, but it did not. You can start upgrading to Windows 10 right off a clean installation of Windows 8.
For clarification, I used a T530 that came with Windows 7 Pro (MBR), updated it to Windows 8 Pro and 8.1, transfered and restored it a few times with dism and changed the bootloader to UEFI in the past years (so there where enough possibilities for something to break the Windows 10 upgrade process). I received a new product key during my Windows 8 upgrade back then, which I used during the installation from the refresh media, however I haven't received a new product key nor do I have any indication which licensing information was used to activate Windows 10 (and will probably be voided by Microsoft for downgrades) yet.
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@Ramhound : " inexperience person like yourself" - what gave me away :-D ? – Lord Loh. – 2015-07-29T02:38:26.740