Every step below is from an official source
Switch from iCloud Mail to Outlook.com
What to do at iCloud Mail before you leave, what Outlook.com needs when you join, and everything else the switch touches. Your full plan is built in your browser and stays there.
Official sources reviewed . How we review sources
At iCloud Mail, before you leave
Forward iCloud Mail to your new addressBefore
At icloud.com/mail, open Settings, select Mail Forwarding, tick Forward my email to and enter the new address.
Automatically forward email in Mail on iCloud.comApple. ReviewedDecide whether to keep forwarded copiesDuring
Select Delete messages after forwarding if you don't want copies kept in iCloud. Keeping copies uses your iCloud storage.
Automatically forward email in Mail on iCloud.comApple. ReviewedExport your contacts as a vCardBefore
At icloud.com/contacts, select contacts, or use the Actions button to Select All Contacts. Then select the Share button and choose Export vCard. This needs a tablet or computer.
Import, export, or print contacts on iCloud.comApple. Reviewed
At Outlook.com, when you join
Forward your other account's mail to Outlook.comDuring
Outlook.com no longer lets you connect new third-party accounts such as Gmail. To read that mail in Outlook.com, set up forwarding in your other account.
Connected email accounts like Gmail and Yahoo not working in Outlook.comMicrosoft. ReviewedImport contacts from a UTF-8 CSV fileBefore
Microsoft's contact import guide, which applies to Outlook.com, recommends a CSV file with UTF-8 encoding so all text shows correctly.
Import or export contacts in Outlook using a .csv fileMicrosoft. Reviewed
Then: everything else the switch affects
The steps above are what iCloud Mail and Outlook.com say. Your full checklist adds the accounts, codes, payments and devices that depend on your email provider, in a safe order. It's built from your answers, in your browser.