When I open my existing solution in Visual Studio 2012 professional, I got the above error. This used to work but something messed up after the computer is rebuilt.
I got this error in TFS2017. For me the problem was a Self-Signed Certificate.
Open the TFS URL in IE and you will see a Red Address Bar:
Click the "Certificate Error" in the address bar:
Then select "View Certificates":
If clicking "View Certificates" doesn't work, right click on page > Properties > Certificates.
If the Install Certificate button is hidden to make it visible you will have to Open Internet Explorer Options > Security > Sites > type the TFS server URL > Tick Require server verification > click Add. (If the dialog is disabled see the guide Trusted Sites Dialog is Disabled at the end of this answer).
Once you have the install certificate button available, select “Install Certificate”.
This will launch the Certificate Import Wizard. Make sure to Choose the option “Place all certificates in the following store” and select browse.
Select Trusted Root Certification Authorities and click Ok.
Click Finish on Completing the Certificate Import Wizard:
Click yes on the security warning to install the certificate.
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Trusted Sites Dialog is Disabled
You can check to see if the site is Trusted, on Windows 7 the path is: HKEY_CURRENT_USER\Software\Policies\Microsoft\Windows\CurrentVersion\Internet Settings\ZoneMapKey
The key should contain several string values with a name indicating the URL and numeric data indicating the zone, one of the following by default.
If the TFS site is not listed in the registry then add it manually. Restart Visual Studio and try to connect to the TFS server again from Visual Studio. Once you can connect you can also remove the TFS server from the Connection List. I suggest removing it and adding the FQDN url which will most likely already have a Trusted Site rule.
Edit
Hit this again. This time it was caused by a problem with a network card that was replaced on the weekend by our telecommunications provider.