Before changing your primary address, make sure you understand the additional changes you may need to make after you make this changes. Refer to the following document for more information: Office 365 - Additional steps to complete when your primary email address is changing.
The instructions below provide steps to change your primary address.
Important: It may take up to 24 hours for this change to be reflected within Office 365 and the Global Address List (GAL).
For more information about the email addresses you see listed on this screen, see: Office 365 - Manage Alternate Email Addresses