Note: Mailbox archive is not a substitute for responsibly managing your mailbox.
admin.exchange.microsoft.com (proper credentials are required)
Select mailbox > "Others" tab > "Manage mailbox archive". Enable archive mailbox for user.
Apply a retention policy to user (default MRM policy is fine). This will apply retention tags to their mailbox. Retention tags are visible to end users and can be used to specify when items in users' mailboxes will be moved to the archive or removed from the mailbox.
Below is what retention tags look like to the end user (below). Use the archive policy options to move to archive mailbox, which should show in Outlook navigation pane. This doesn't happen instantly, but policies will be applied in time. I added a "90 days" option to the archive policy. These tags will move email to the archive mailbox if older than "x days / years", according to the tag.
Retention policy is a separate policy. It does not move to archive mailbox, it deletes.