They don't publicize it too much, and there are some tricks to get it working as needed, but the documentation is below.

https://developers.google.com/custom-search/docs/overview

Just a note, it does not return identical results to the Google web search, it is a slightly different search index. Although now there are several companies that sell directly scraped Google SERP results. I believe that they do operate in potential violation of Google's TOS though.