Eclipse is Java based and packages all the necessary tools with it but it is extremely debatable whether that means it "works fine" anywhere...

But to address the grandparent post a bit more directly, in my experience Android Studio runs great under both Windows and Linux, I've used it frequently on both with no complaints.

The instant run feature this new canary build has will be welcome since the deploy->run cycle has always been just slow enough to feel like a bottleneck to me, though I never faulted Android Studio for this.