How to find 3rd party app developers for our API?

My company is developing a web application and we are about to release a developers API soon. We would like to promote our API to 3rd party developers so that they develop their own applications around our API. We even think of holding a developers contest with a prize for the application that created the most users.

Where should we promote our API and our contest? How can we reach big developer communities?

Some users of your application will be the initial developers using your API. They are looking for a way to use your tools without being locked down to your choice of GUI. They want to automate their process.

So reach out to your users for the contest.

Check out Mashery and Programmable Web (I am sure there are many more similar sites) - these are in the business of developing & promoting APIs.

I agree with all of the comments above and would also like to suggest that you post something about it on reddit. there are tons of programming/developer subreddits and I'm sure someone would love to jump on it.