Rise of the Tomb Raider will be published by Microsoft, not Square Enix. The news was confirmed by Xbox marketing director Aaron Greenberg.
@diosmekemeke Yes we are publishing Rise of the Tomb Raider.— Aaron Greenberg (@aarongreenberg) December 8, 2014
We still don't know if the game will come to platforms other than Xbox One and Xbox 360. It was suggested by Phil Spencer that the game had a period of exclusivity, but given that Microsoft are publishing the title, it could be that we won't hear any confirmation of other platforms for quite some time, it at all.
Losing Tomb Raider will likely be a blow to PlayStation fans, although they have Uncharted 4 to tide them over, so it's not all bad news.
Also we still have a suspicion that it's a timed release, although that's just a hunch rather than inside information.