As of Tuesday, March 31, 2015, all registered Apple developers can submit new apps and updates containing WatchKit extensions to the App Store.
If you need help, Apple has published instructions on its WatchKit site to help you prepare the required materials. Good luck to all!
Historical
As of March 9, 2015, Xcode 6.2 with WatchKit has officially been released, and you may now submit apps to the App Store that utilize the iOS 8.2 SDK.
However, builds that include WatchKit targets are not yet accepted:
Please Note: Apps built with Xcode 6.2 and iOS 8.2 SDK may be submitted to the App Store. However, WatchKit extensions are not accepted at this time.
If you try to submit a build through Xcode, you will be presented with an error about multiple executable binaries in a project (currently, only one is allowed – your iOS app).
It appears that Apple has begun accepting updates including WatchKit apps from select high-profile developers, but this is not yet available to all.
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Apps using WatchKit target iOS 8.2, which has not yet been released. Apple has not yet announced when iOS 8.2 will be released, and Xcode 6.2 (the only environment where WatchKit apps are supported) is still in beta.
Because of this, you will not be able to upload any builds containing WatchKit app targets until Xcode 6.2 is officially released (you can't upload builds to iTunes Connect from beta versions of Xcode).
Once it is released, you will be able to upload your build, and the iOS portion of your app will continue to run on the earliest target you have set for your project (i.e. if your app targets iOS 7, it will still support iOS 7 with your watch app included, but the watch app will not be available to iOS 7 users: it works like any other extension).