While Gradle is a great building tool some concepts natural to a Maven user are not (yet ?) part of the basic package. One of them is the provided scope.
Gradle is very flexible and this missing feature is quite easy to implement: Google gradle and provided scope will give you many hints on how to implement this. However when it comes to make it works with IntelliJ Gradle plugin things can be a little bit more complicated.
After some try and fail cycles I came to the configuration below that works fine with IntelliJ:
It is working with Gradle 2.0 and IntelliJ 13.1.4 and in the project structure, the compile and provided dependencies are correctly configured.