Please note that this is a two step process.
Step 1: Setup MFA on your mobile device
Step 2: Change the default authentication method to the Microsoft Authenticator app
Go to mysignins.microsoft.com and then click Security Info on the left:
Do not use Safari as it will not display the content correctly.
Click on Add Method
Select Authenticator App. Click Add
This screen will direct you to download the mobile app. Click Next
Click Next
Download Microsoft Authenticator app on your mobile device
Note: unlike some other apps, the Microsoft Authenticator app is dedicated to authentication and will only ever send you notifications for sign-in events.
Open app and click + to add account
Select Work or school account
Click scan QR code
On website: Scan QR code with phone
Note: Don't scan icon below. You will need to scan the QR code for your account.
Click Next and you should receive a push notification on your phone. Click Approve on your phone and then Done on the screen below.
When you return to the Security info screen, you will see the "Authenticator App" method has been added..