I have written this blog detailing processes to sync your local active directory with Azure.

You can sync Azure active directory with your existing local directory as follows:

Step 1- Login to Azure management console

Azure management console AD user migration from Local DC to AAD

Step 2- On left hand pane, Click New

hand pane AD user migration from Local DC to AAD

Step 3- Create new Azure Active directory
Under the User tab, create user with a specified domain such as test.onmicrosoft.com. This should be unique. If you already have office 365 active directory, then you can opt for the “existing directory” option.

azure active directory AD user migration from Local DC to AAD

Step 4- The user will appear as User@test.onmicrosoft.com

This user must be a Global Administrator in role. We can have a custom domain such as somedomain.com instead of somedomain.onmicrosoft.com. Custom domains should be verified with domain registrar with TXT record provided on Azure portal.

Azure portal AD user migration from Local DC to AAD

Step 5-Now go to the domain controller from where you want to sync all users in   cloud directory. It is recommended to use a domain attached windows server with OS version 2008 and ahead.

Step 6-Now download dirsync tool (better known as WAAD sync tool) which is also available from Azure portal links.
Activate sync from Azure management portal

Azure management services AD user migration from Local DC to AAD

Step 7 – Download and install this on domain attached server. It will prompt for domain enterprise admin credentials (AD DS) and Azure Active Director Global administrator.
Put the right entries and your local directory users will sync on Azure active directory.

Azure cloud services AD user migration from Local DC to AAD

When you are done with all the steps successfully, you can view all users on your Azure Active Directory.

References: https://msdn.microsoft.com/en-us/library/azure/dn144766.aspx