This is a common request and complaint across all of Salesforce Customers, even in Enterprise and Unlimited Edition. By default, Salesforce does not automatically deliver this behavior, even though it's an outbound email from within Salesforce. But, the good news is, there is a simple workaround to help you achieve your ultimate objective, gaining visibility on the record when an alert has been sent. Follow these steps:

  1. Go to the Workflow Rule that's producing the Email Alert that you want added to your Activity History
  2. Click on Edit
  3. Go to the Workflow Actions section and add a "Create A Task"
  4. Name the new Task the same name as the Email Alert Subject
  5. Set the Status field to "Completed"

The results of adding and additional Workflow Action to this Workflow Rule will be exactly what you're looking for, minus one thing. The Email body from you alert will not appear on this task. If you'd like you can paste your email template to the comments section of this new Task. But if you have any merged values in your email template, they will not appear within your Activity History for this new task you just created.