To sync any Microsoft cloud service or corporate Exchange calendar with Android, you can use Android's built-in Exchange sync. This is provided and updated through the Gmail app.
Go to Android settings - accounts, there create a new account.
Select Exchange as account type, then make sure to select manual configuration.
Use m.outlook.com as server for MS cloud services.
Limitations of MS Exchange Sync in Android
Some device manufacturers have limited sync of past events, sometimes this is configurable in the account settings or Gmail app settings (coupled with the synchronization of past emails).
Android has no native support for Outlook/Exchange categories, but we are currently working on integration of the proprietary category data provided by most Exchange integrations.
Android has not support for attachments in MS Exchange.
Android has not native support for the availability field out-of-office, but we are working on support for proprietary solutions if implemented by the phone manufacturer.
Double or Triple entries in MS Exchange calendars
Lately, several users reported duplicate entries, in their Exchange calendars. This can be solved by removing and re-adding the account in Android account settings.
Exchange Calendar missing after restart on Samsung device in Ultra Power Saving Mode
Unfortunately, you need to remove and re-add the account if this happens. If your device is affected by this firmware bug, please contact Samsung support.
Outlook Sync issues since November 2019 Gmail Update
The November update for the Gmail App (which provides the MS Exchange sync-adapter for Android) seems to break Outlook synchronization. Downgrading to an older Gmail version seems to fix this issue. See here for details answers.microsoft.com