We're strongly encouraging users to move toward the Gradle build system, and we're in the slow process of making that the only way to create new projects in Android Studio -- you're seeing this now on importing Eclipse-based projects. We'd like to replace all other build systems in use with Gradle, including Ant and the Eclipse internal builder, though the latter two are farther out on the roadmap.
If your ultimate goal is to move to Android Studio, then you might want to reconsider and just set up a Gradle build file. You don't have to adopt the Gradle-style multimodule project structure (which the current Eclipse importer imposes upon you by making a copy of your project); you can rework your build.gradle file to use the Eclipse-structured project in-place. You can get a good start on this if from Eclipse you use the feature to export your project to Gradle build files. It will set up the project in that fashion, though that feature in ADT is a little out of date and you'll need to update the version of the Android Gradle plugin in the build file and the Gradle version in the wrapper that it outputs.
I think this may actually solve your problem. IntelliJ or Android Studio have never been able to use the Eclipse project directly -- they've always imported the Eclipse project and converted to an IntelliJ-style project, and if you later change the Eclipse project, you'll need to re-import into IntellilJ-land. I'm guessing your real desire is to use the Eclipse project in Android Studio without having it make a copy and converting into its preferred directory structure. (By the way, we'll eventually improve Eclipse-to-Gradle import to lift this restriction).
Once you have the Gradle build file in place, you can use it when working with the project in Android Studio, and you'll still have the Eclipse project files when working with it in Eclipse. The big drawback is that you'll have to keep them in sync as you change dependencies and project structure, but hopefully that doesn't happen too often. Even if you weren't using Gradle, you'd still need to keep both projects in sync anyway, so Gradle isn't costing you anything there.
Having said all that, it doesn't directly answer your question, which is how to use the your project without Gradle.
Once you have an IntelliJ-built project, you can open it in Android Studio and use it normally without migrating to Gradle (though I think it does show you a popup when opening the project recommending you do so; you can ignore that). What you need to do is to get that initial IntelliJ project, and once you have it, check all the .iml files into source control -- those .iml files contain all the project information. To get those files, you'll need to import the Eclipse project either in IntelliJ CE, or in Android Studio prior to 0.4.0. Then you'll have your .iml files -- hang on to them.
I'll point out that if you're using Gradle as your build system, we recommend that you don't check those .iml files into source control. There, the build.gradle files are the source of truth for project structure; the fact that Android Studio creates .iml files at all is an implementation detail that reflects that internally Android Studio is still treating this project as an import instead of deriving structure from the Gradle files directly (and we resynchronize state when we know we need to). But saving those .iml files into source control or modifying them directly will lead to confusion or loss of any changes you make there when it resynchronizes.
