Technically you should be able to use it since they are world phones and have radios for both GSM and CDMA. The problem you are going to have is getting Verizon to allow it. AT&T and T-mobile will allow you to use your Verizon phone on their network. All you have to do is give them the MEID. They will even provide the APN settings for you if you ask and they are on their website.
Verizon however, is reluctant to allow ESNs that are not on their list. Same with Sprint. It isn't impossible, but you will have to jump through some hoops. There are forms to be filled out, similar to the one's to reinstate an ESN that has been flagged. It's been a while, but I believe you're looking at about a 3 week wait to see if it's approved, if they even allow you to submit the forms. I know people that have moved their Sprint phone over to Verizon, but in the end, they all agreed that it wasn't worth the hassle and they would never do it again.
EDIT: Now that I'm thinking about it, I'm not 100% sure if the AT&T and T-mobile versions have CDMA and LTE antennas. Verizon's version has them all. It doesn't really make sense for Verizon's to get GSM antennas while the other's don't get CDMA or LTE. Then again, Verizon's was a modified version to allow wireless charging, so it wouldn't be out of the question.