Migrate Mailboxes on Office 365
Organization can migrate email to Office 365 from other systems. Your administrators can migrate mailboxes from an Exchange Server or from migrate email from another email system. And your users can import their own email, contacts, and other mailbox information to an Office 365 mailbox created for them. Your organization also can work with a partner to migrate email.
Before you start an email migration, review limits and best practices for Exchange Online to make sure you get the performance and behavior you expect after migration.