You can, though it might require a little finessing to get Verizon to activate it for you. it's technically possible, but some people have said they ran into some difficulty, partly because Verizon tracks their inventory and hems and haws and activating a device that's not in their database. It CAN be done though.
The opposite (Verizon iPad to T-Mobile) works perfectly and effortlessly. I did it. But T-Mobile is happy to activate an iPad not "branded" to their network as long as it's compatible.