While I'm sure no one knows the answer to your question at this time, I can summarize all the information there is on the Internet regarding this, as I have done a good amount of research into this topic.
Assuming you have a Retail License, there are a few answers from the Internet. Before that, though, I would like to quote the Section 4 Part B of the Terms for Windows 10.
If you acquired the software as stand-alone software (and also if you
upgraded from software you acquired as stand-alone software), you may
transfer the software to another device that belongs to you. You may
also transfer the software to a device owned by someone else if (i)
you are the first licensed user of the software and (ii) the new user
agrees to the terms of this agreement. You may use the backup copy we
allow you to make or the media that the software came on to transfer
the software. Every time you transfer the software to a new device,
you must remove the software from the prior device. You may not
transfer the software to share licenses between devices.
The issue is that the terms do not specify how to go about transferring the license to new hardware. It also doesn't specify whether or not there is a time-limit (more on this later). Now that we have what the official terms say, below I summarize what others (including Microsoft Officials, whose words are obviously not legally binding).
For completion, I will include here the answer by Microsoft Rep basically re-quoting the Terms in a different way. He states that if you upgraded from a retail license, you retain the transfer rights. But he does not specify how to go about doing so (and that is the question we all want to know...).
Because I don't have enough reputation, I cannot post more than 2 links. So, the links to the sources of the Scenarios are posted in the comments, in order.
Scenario 1 : There is a Time Limit
Basically, you are free to install your retail key of Windows 7 to any machine and upgrade it to Windows 10 before 2016.07.29. After that, the machine you have the upgraded version of Windows 10 will still be usable, but you can no longer upgrade to Windows 10 from your Windows 7 key. That is, if you install Windows 7 using your key to any machine (including the machine already running the upgraded Windows 10), you will not be able to upgrade.
Scenario 2 : There is no Time Limit, but Machine Limit
In this case, there is no time limit. You can upgrade to Windows 10 from your Windows 7 key, provided that you do it on the latest machine that Windows 10 is installed on before 2016.07.29. In other words, after 2016.07.29, the machine that the upgraded Windows 10 is installed on will be able to upgrade to Windows 10 should you install Windows 7 on it again. However, this will NOT apply to any other machine you install that same key of Windows 7.
Scenario 3 : There is no Time Limit, and no Machine Limit
In this case, there is no time limit, and also no machine limit. Basically, once you "take" the Windows 10 upgrade from a Retail License, you have it forever. The Microsoft Server will associate your key with the fact that you have accepted the Windows 10 Free Upgrade offer. In other words, you are now able to install your Windows 7 key on any machine (even after 2016.07.29), and then be able to upgrade to Windows 10. Note here, you have to go from Windows 7 to 10, you cannot just install Windows 10 and use your Windows 7 key. Also note, the source of this scenario is the same as that of Scenario 2, and the poster of this information is also the same guy! So I'm not sure what he's cooking. But he is a Microsoft Rep.
Scenario 4 : The Previous Key Works
At this time, I cannot find the source of this. But I'm sure you've already seen this. Apparently, you can use your Windows 7 key to install Windows 10. But some people claims this does not work. One possibility (if this scenario is correct) is that you have to upgrade to Windows 10 through Windows 7 at least once, and THEN you can use the key. I have not tested this, and I have not seen other people test this (correct me in the comments and I will update). It is very unlikely this is the correct scenario though.
In conclusion, I think either Scenario 1 or Scenario 2 is the most likely case.
Install W7 again, activate, then upgrade to W10 again. – Moab – 2015-08-25T00:23:45.567
2If your old Windows 7 was an OEM version, you'll need to buy a new license for Windows. – ChrisInEdmonton – 2015-08-25T00:31:39.430
1@ChrisInEdmonton as I mentioned in the answer below, you can activate the OEM key on a new motherboard, but the trick is you have to use the automated activation system by physically calling Microsoft. I've done this several times after replacing a failed mobo, or by upgrading to a new one. I've never once been denied activation. – DrZoo – 2015-08-25T02:30:25.583