Import existing email messages to your custom iCloud Mail address on iCloud.com

If you add a custom email domain you already own to iCloud Mail, you can use iCloud.com to import existing email messages from your previous email provider (not available for all email providers).

Important: Make sure you have enough iCloud storage to import all your email messages. See Check your iCloud storage on any device.

Go to icloud.com/icloudplus, sign in to your Apple Account (if necessary), then click Custom Email Domain.
Tip: If you’re already on iCloud.com, you can also click in the toolbar, then click Custom Email Domain.
Select a domain name, scroll down, then click the “Import mail” button (or click next to Import Mail to import email messages from an additional address).
Follow the onscreen instructions to sign in to your previous mail account.
It may take some time to import all your email messages. They appear in an iCloud Mail folder with the name of your email address. If you had your mail organised into multiple folders in your previous email account, those folders appear inside the new folder.

You can also manually move email messages to iCloud Mail using the Mail app. See Organise email in mailboxes on iPhone, Organise email in mailboxes on iPad or Move or copy emails between mailboxes in Mail on Mac.

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iCloud User Guide

Import existing email messages to your custom iCloud Mail address on iCloud.com