According to Frontier, Elite: Dangerous is going to be released next month on Xbox One. At the moment the game is a part of the console’s Preview Program, and you have access to an in-developement build.
Elite: Dangerous will be released on October 6th, as the Frontier’s CEO David Braben, recently confirmed. Also, he said that only some of the ships and the modules from the Preview will be included in the full game too. In the future you will also have the possibility to account transfers across PC and Xbox One.