It is not the official Kodi media player but a port that is missing some features. Still, XBMC/Kodi enthusiasts will surely recognize MrMC, which is now available to download in the App Store on Apple TV for $5.99.
MrMC to Apple TV
MrMC is a "port" of Kodi without the option to install add-ons and change skins. Besides that, it does exactly what you expect from Kodi. It is a media player app that allows you to stream movies, TV series, music and other media formats to the TV from a PC or hard drive. In that way, it is an alternative to Plex and Infuse that are already available on Apple TV.
MrMC uses the classic Kodi interface and works the same way. It is possible to stream video files that are stored directly on network-connected hard drives in your home. MrMC does not require a server application, like Plex does. It can connect directly to network drives via NFS or SMB. The first time you start the app you simply have to set it up to point at the network directories.
As mentioned, add-ons have been removed to make it compatible with Apple’s guidelines. However, it should still be possible to use PVR add-ons. Picture quality goes up to 1080p and several audio formats are supported via passthrough. Subtitles are also supported. The developer has not released a lot of information so it is unclear what else is there.
MrMC is available in the App Store now for $5.99. The app will be released for iPhone and iPad later.