In an on-premises environment an admin can use the New-MailboxImportRequest cmdlet to import a batch of PST files to a mailbox or even directly into the users In-place Archive mailbox with the -IsArchive switch. Currently this is not possible with Exchange Online.
Of course there are some alternatives, such as an Outlook based manual import.
However, if your organization wants to move away from PST, and you should, then a manual process may not be the best solution.
When Microsoft bought the PST Importer tool from Red Gate and re-released it in 2012 as PST Capture (and more recent as PST Capture 2.0) it looked like this would be the perfect tool to locate and import PST files. Unfortunately the tool has severe shortcomings, most important areas are features, stability, performance and the fact that the tool is not supported through Office 365 Support.
So it is great news that Microsoft is working on providing...
The ability to import data into Office 365 in a quick and easy manner has been a known constraint of Office 365, and a solution for this issue has emerged as a key request from customers. The engineering team has been working on a solution that will allow quicker imports of data into Exchange Online Archive Mailboxes. You will now be able to import Exchange Online data through PST files into the service without using third party tools.
The announcement continues with the mention of Drive Shipping and Network Based Ingestion:
Drive Shipping and Network Based Ingestion options will use Azure-based services to import data. Over time we will be extending this to other data types across Office 365.
Imagine you would be able to ship a 4TB USB drive to Microsoft and have them import your files to Exchange Online or SharePoint Online!
Expect the experience to be quite different from what you would do on-premises. Because the actual import process is handled by the Mailbox Replication Service (MRS) it won't be possible to have your local files imported into Exchange Online with the New-MailboxImportRequest cmdlet. Instead expect in interface to upload (or ship) your files to an Azure datacenter and start the import process from here.
Note that the announcement specifically mentions Exchange Online Archive Mailboxes. I hope it will be possible to import the data to the primary mailbox too to facilitate scenarios where that makes more sense.
If you want to be the first to know what Microsoft has in the pipeline for Office 365, make sure to keep an eye on the Office 365 roadmap.