Solution: Waiting for Approval from Another Device

After updating my iPhone to iOS 10.3 and macOS to 10.12.4, I was told that I needed to re-sign into iCloud in order to continue using some of the provided services. After going past a certain point in the process, I was then told that I needed to approve each individual device from another trusted device that was already signed into iCloud. The only issue was that no matter which device I tried to approve, I always found myself staring at a window that said "waiting for approval from another device" -- and none of my other devices ever received any type of prompt. This was happening because of two-factor authentication.

Taking to Google, I found a lot of people with the same question. Many said it was a Keychain issue, but since I couldn't sign into iCloud, Keychain was turned off, so scratch that. I tried going to appleid.apple.com and turning off two-factor authentication. I reset my security questions and all of my devices were then able to sign back into iCloud, but when I turned 2FA back on, I got to a certain point in the process and then hit the same "waiting for approval" wall. I did not want to reset any iCloud data, which was why I kept putting off the 2FA process.

I finally called Apple Care and was on the phone with two different people for 2 hours, but we solved the issue. What finally ended up working for me was this:

1) Go to appleid.apple.com and turn off 2FA. You'll then be asked to reset your security questions. Make sure you save your changes

2) Go to all devices logged into iCloud under your Apple ID and sign out of iCloud

3) Sign back into iCloud on all of your devices, one at a time. If you want, check the status of 2FA at appleid.apple.com after each device is signed back into iCloud, just to be sure that 2FA isn't automatically turning itself back on

4) Once the last device has been signed back into iCloud, turn 2FA on again at appleid.apple.com. Save your changes, and then your devices should prompt you to go ahead with the authentication process, at which point I had no further issues.

After signing back into iCloud, I also needed to setup iMessage, FaceTime, text message forwarding, etc for devices that weren't my iPhone.

Hope this helps!