This article has been moved to its new home here: https://benperk.github.io/msdn/2016/2016-03-how-to-find-you-outgoing-azure-app-service-ip-address.html
If you have ever wondered how to find the outgoing IP address of your Web App, Mobile App, API App or Logic App, look no further.
To see how to find the OUTBOUND IP ADDRESSES from the Azure portal, view Video 1.
Video 1, find outgoing, outbound IP addresses from the portal
You can also capture them from the Azure Resource Explorer here, then navigate to the information as discussed in Video 2.
Video 2, find outgoing, outbound IP addresses using the Azure Resource Explorer
possibleOutboundIpAddresses -> if you are using Pv2 as announced here, there may additional outgoing IP addresses allocated. Perhaps 1 or 2 additional. When I scaled, I did not get them and remained at 4. Keep that in mind if you scale from version 1 (Premium, Standard, Basic, etc...) Premium V2 that these IPs may be added added. If they are added, you will see them in the portal or in resource explorer.