This blog outlines the different methods of data migration and use cases. Your method of migrating data to the cloud will depend on many factors. Migrating large amounts of data can be done with any of the methods explained in the blog, including Azure Data Box, File Shares, Site Recovery service, and more.
Just move it to the cloud
How you migrate your data to the cloud depends on many factors, but @Microsoft is here to help. Learn from this blog post about different methods of data migration and which one may be best for you.