Minecraft: Xbox 360 Edition developer 4J Studios is working on a way to allow Xbox 360 players to transfer their world saves to the Xbox One version of Minecraft when it releases.
.@stampylongnose We’re working on ways to move Xbox 360 saves to Xbox One with Microsoft. Can’t say it’ll be there until it’s 100% working.
— 4J Studios (@4JStudios) November 15, 2013
4J is currently working on versions of Minecraft for Xbox One, PlayStation 4, PlayStation 3, and PlayStation Vita. There’s no release dates for any of these versions at the moment.