No,you can't use your T-Mobile network service on Verizon phone.Because T-Mobile is GSM,Verizon is CDMA.
But you can use your T-Mobile network sim card to other GSM based phones.But your phone should be unlocked one.If is' locked,you will need to unlock your phone.For unlocking visit OnlineGSMUnlock.com I hope it will be very useful to you.