A couple of weeks ago, a release candidate for Android Studio 1.0 rolled out to the Canary development channel to allow users a chance to poke and prod at it before an official launch. The serious issues have been worked out and Android Studio has been given its first official release to the stable channel. Alongside the title change, Android Studio has also been declared the "official Android IDE." ADT with Eclipse is still available, but is no longer considered to be in active development.
Aside from a few bug fixes, this version doesn't contain any significant changes from the recent release candidates. However, developers choosing to stick to a single version and avoid the aggressive update schedule –and changes to the Gradle plugin– should jump onto this version for more consistent support. Updating from either RC1 or RC2 is pretty quick, and the patch should come in below 10 MB. However, there is also an update to the SDK Tools package that users will be prompted to download shortly after restarting on 1.0, and that will take a little longer.
Now that Android Studio has been coined "The official Android IDE," Eclipse with ADT has been pushed mostly out of view on the developer portal. There are still download links and resources for developers that need to use Eclipse with the NDK (Native Development Kit), but there are messages on a few pages to indicate that the ADT plugin (for apps that rely on the SDK) is no longer in active development. This means that it's possible there may be occasional bug fixes to resolve critical issues and keep it operational, but there will probably never be any new features added, and the ADT plugin may be completely abandoned in the future.
If you've been using Eclipse with ADT, be aware that the ADT plugin is no longer in active development, so you should migrate to Android Studio as soon as possible. For help moving projects, see Migrating to Android Studio.
Congrats to the Tools team for hitting this major milestone. Android Studio has grown up significantly over the last 18 months, and now it has the seal of approval from Google.
Alright, developers, go download the update and get back to work.