How do I terminate my contract?

My 2-year term expired, so I guess now I'm on month-to-month status. I'm going with a different carrier, and get a new phone with them. I was told by my new carrier to just bring the contract number, and they do the switchover with my current SIM, I get to keep the same number. So does my TMobile service automatically end once the SIM is in a new phone with the new carrier? Or do I need to inform TMobile first, have TMobile end my account, then go to the new carrier to start the sign up process?

Thanks,