Use the built-in iOS mail app
Tap Settings > Mail, Contacts, Calendars > Add Account.
In the Add Account page, tap Outlook.com.
Note This includes international domains like @outlook.co.uk or any custom domains hosted on Outlook.com.
Enter your full email address and password, and then tap Next.
By default, Mail, Contacts, and Calendar information are synchronized. Tap Save.
Not working? Make sure you entered your email and password correctly and try again.