Updated 6/7/17 with additional information. Fixed a few links on 6/28/17.
After you've removed any configuration issues that might block your migration from Intune groups to Azure Active Directory (Azure AD) groups, you may be wondering how you'll know you've been migrated. Here's what to look for.
When you first open the Silverlight Intune console at http://manage.microsoft.com after migrating, you should see the informational message below that says "Preview the new Intune portal in Azure", and if you click Azure, it will take you to http://portal.azure.com. That's your first clue.
If you missed that, you can be 100% sure you've migrated if you try to create a new group in the old console and you can't!
We retry all blocked migrations every 24 hours, but depending on how complex your account is, it may take a few days to create all the new Azure AD groups, remap all of your policies, terms and conditions, and apps to the new groups, and then verify that we got everything right. After everything is validated, your migration will finalize and you'll see the evidence above.
We have a tiny fraction of accounts that don't have any configurations that block migration, but are still blocked because something isn't adding up in our validations. We have to check each and every account very carefully and make sure everyone migrates without any errors, so it may still take some time before your account finishes the migration process. Please know that resolving any issues with your migration is very important to us. We're sorry for any delays. We are all working hard to get you onto the new Intune on Azure experience as soon as possible!
Finally, you may see a message in Intune on Azure saying "We're not ready for you yet". If you see this message, it doesn't mean you haven't been migrated. There are a few feature areas that required their own data/policy migration from the classic console to the new console, such as iOS Device Enrollment Program (DEP). You can see a full list of items here: https://aka.ms/intune_stillworkingon.
Here's several post-migration guides: