Microsoft has announced a new Office 365 Migration API that moves files through Azure using a dedicated path. Previously, when you used migration tools such as ShareGate, AvePoint, Metalogix, etc. the migration tools used the same conduit that the Office 365 portal uses to migrate files. Microsoft throttles that path to avoid the Office 365 portal being slammed by people migrating their content.
Using the new Migration API, you can package up exports of your current SharePoint content and send them through Azure which will then import the content into Office 365. This will work for SharePoint files, file shares and personal file shares.