Avid calipers & Shimano rotors – will they work?

I’ve got centrelock wheels & rotors, and currently run XT775 calipers. Nice brakes, but I still find the faffing of hydraulics a pain compared to Avid Mechanicals. What I’d like to do is keep the nice (tarty XTR) rotors (180 up front, 160 rear) and use them with the Avid Mech calipers. So, can this be done? Are the rotors the same diameters & thickness, or is there some reason it’ll all go horribly wrong?

Cheers.