I have the code written which is using envelopes to request a signature from the client like in this tutorial:
https://www.docusign.com/developer-center/recipes/requ
There are two possible ways to do this.
One is to set up an account wide Connect Configuration within the DS WebApp, this will send the requested event notifications on every envelope sent/completed to the URL: https://www.docusign.com.au/sites/default/files/connect-guide_0.pdf#page=5
You can also define this per envelope with the eventNotification parameter. However, the parameter is not baked into the provided recipes. EDIT: I stand corrected, see Larry's response below https://www.docusign.com.au/p/RESTAPIGuide/Content/REST%20API%20References/Send%20an%20Envelope.htm