Outgoing IP address for Azure App service are different than the incoming IP address. To clarify the difference, the incoming IP address (as the name would indicate) identify the IP address using which data could be sent to App Service. This is what you would see when you would typically do DNS resolution for the App Service. Outgoing IP address identify IP address which would be used when sending data from Azure App service to the outside world. You may need this info because you may need to protect your environment from threats or white-list certain requests.
To identify outgoing Azure App Service IP address, we can simply navigate to the https://portal.azure.com and then go to the app service in reference. Once its selected and show the overview information, select properties. This will open a new panel to show the properties of app service where you can find outbound IP address:
You can also get same information using Azure PowerShell as well. For that, first login with Login-AzureRMAccount cmdlet and set your subscription. Then we can run below PowerShell command:
Get-AzureRmWebApp -Name <app-service-name> -ResourceGroupName <resource-group-name>
Below is one of the sample runs: