Maintenance for the week of May 25:
• PC/Mac: No maintenance – May 25
• ESO Store and Account System for maintenance – May 27, 6:00AM EDT (10:00 UTC) - 4:00PM EDT (20:00 UTC)
Yes it is possible to login on a new Xbox console. You will need to login with the same ESO and Xbox linked accounts you were using on your previous console.