When you switch to Office 365 email from another service such as Gmail (or Yahoo! or AOL) you can bring your old email with you and manage it in Outlook. This way, you can have all of your email—past and present—in one place. There isn’t a one-click button to import your Gmail, but the desktop version of Outlook has a wizard that will walk you through the steps.

Walkthrough: https://support.office.com/en-us/article/Import-Gmail-to-Outlook-20fdb8f2-fed8-4b14-baf0-bf04b9c44bf7