Recently I worked with one of Microsoft's accelerator startups to migrate their Parse application to Azure.
We followed these instructions to move their hosted Parse application to a Node.js express app very easily, running as an Azure Web App.
As part of this process, we also explored ways to migrate the Push Notifications service from Parse to Azure Notification Hubs. In this process we developed parse-to-anh which is a Node.js module that can be used as a command line tool or as a module as part of a larger migration script.
The tool currently supports migrating ios and android users.
Note for Android users- One thing you should be aware of is that Parse uses their own GCM SenderId to send push notification to android users. The intention was to hide the hassle of on-boarding with Google Push Notification service. For you to be able to migrate these users, you'll need to follow these instructions (look for "Exporting GCM Registration IDs"), to create your own SenderId and to update your existing app to register the devices against Google, so that on migration time, the token will match your SenderId. This should be done ASAP- so that hopefully most of your users will get the app update and will register with your SenderId.