MailChimp has a very cool API that allows you to add/remove addresses on a mailing list.

Take a look at the sample code here: C# Solution | PHP Script

Notice the line where we can get the order's email address.
Below this line you can pass this email address to the MailChimp API.
You can use any programming language with the MailChimp API. They offer sample code in PHP and ASP.net

Want to go further?

You can also add people to different mailing lists based on the products they ordered.
In the C# solution we show you how you can iterate through the line items in the order.
Basically you can do something like
if (item.Title.ToLower().Contains("lion king"))
// Add them to the Lion King newsletter