How can I manage server to server communication for membership payments?

[dlepage99]

Here is what my application needs to do:

1. Client on my application hits a buy button to pay for a membership.

2. The Buy Button information contains an identifying order number that was created on my application and directs the client to Shopify to process the payment.

3. Upon completion of the payment Shopify sends back information to a URL within my application with the order number that my application had generated and sent to Shopify with the Buy Button as well as  a flag indicating either a successful or unsuccessful payment.

4. My application then performs the appropriate updates to the membership database.

This type of activity is handled well within Paypal and Moneris and presumably with other eCommerce/payment portals. 

Can Shopify handle this and if so how? I would appreciate any details anyone could provide.