Check that you have the correct phone number associated with your account:
Devices using iOS 7.0.3 or later: Tap Settings > iCloud > Account, then tap Keychain. Check that the phone number listed under Verification Number is correct. If not, enter another phone number.
I'm using a new MacBook Pro, and I, too, waited about half an hour and didn't get any E-Mails or Messages on either my iPad Mini or my iPhone 😕, so I searched for "waiting for approval from other device" on this web site.
I have iOS 9.2 on my iPhone 6, so the path down to "Keychain" is slightly different. Once I found it, there was no spot for "Verification Number", but once I signed into the Keychain using my Apple ID password, it asked for approval for my MacBook Pro, and everything was OK from there on. ✅