The process of Cutover Migration to Office 365 is explained here
The administrator communicates upcoming changes to users and verifies domain ownership with the domain registrar.
The administrator prepares the servers for a cutover migration and creates empty mail-enabled security groups in Office 365.
The administrator connects Office 365 to the on-premises email system.
The administrator migrates the mailboxes and then verifies the migration.
Grant Office 365 licences to your users.
The administrator configures the domain to begin routing email directly to Office 365.
The administrator verifies that routing has changed, and then deletes the cutover migration batch.
The administrator completes post-migration tasks in Office 365, and optionally decommissions the on-premises Exchange servers.
The administrator sends a welcome letter to users to tell them about Office 365 and to describe how to sign in to their new mailboxes.
For more details, visit : www.office.com/setup