Exchange 2013 has new and impressive administration center that allows you to handle tasks such as mailbox moves. I prefer using the Exchange Management Shell for such a task.
Using the following command you can move all mailboxes within a database to your new mailbox database: Get-Mailbox -Database “Source-Database” | New-MoveRequest -TargetDatabase “Destination-Database”
To get info on the migration progress you can use the following command syntax: Get-MoveRequestStatistics -MoveRequestQueue “Destination-Database”
Once this migration has completed you can check if anything exists in the source database with the following: Get-MailboxDatabase -Identity “Source-Database” | Get-Mailbox