The Long waited utility for migrating On-Premises File Share or On-Premises SharePoint server site to Office 365 SharePoint Online is release recently from Microsoft.
This utility/API is PowerShell cmdlets and its called “SharePoint Online (SPO) Migration PowerShell Cmdlets”.
SharePoint Online (SPO) Migration PowerShell Cmdlets public preview is a new API dedicated to migrating data from on-premises file shares to Office 365. To join this preview go to SPO Migration Preview.
SPO Migration PowerShell cmdlets are designed to move on-premises content from file shares and SharePoint Server libraries and One Drive to SharePoint Online and OneDrive for Business. Requiring minimal CSOM calls, it leverages Azure temporary BLOB storage to scale to the demand of large migration of data content.
The detailed information can be found here,