The DT880 is a reference headphone. Superb for reference music listening. They are not a totally sealed design for monitoring purposes if that's of any importance but they would work.
If you need a sealed headphone the AKG 271MKII are superb especially for monitoring vocals and are suited specifically for studios with its auto-mute feature. You get different cabling options out of the box as well (XLR, 1/4", 3.5mm). The 271 don't have the bottom end and crazy detail (not the unnatural detail you get from Grados) of the DT880 but they nail the midrange and even more importantly the upper midrange.