The process for moving probation supervision from one state to another runs through the Interstate Compact for Adult Offender Supervision, which is the formal agreement that allows states to transfer supervision of probationers and parolees across state lines.
The first step is for your brother or his attorney to contact his Florida probation officer well before his release and formally request a transfer of supervision to Tennessee. The Florida probation office will evaluate the request and, if approved, submit it through the interstate compact process to Tennessee's probation authority. Tennessee then has to accept the transfer before anything is finalized. This back-and-forth takes time, sometimes several months, so starting early is important.
Tennessee's probation office will want to verify that the living situation you are providing is stable, drug-free, and not in proximity to known criminal activity. They may conduct a home visit before approving the transfer. Having a clean, stable home ready and being able to demonstrate that matters.
Once transferred, your brother will report to a Tennessee probation officer rather than a Florida one, but the conditions of his probation remain the same. He does not get a fresh start on the terms just because the state changed.
Start the conversation with his Florida PO as soon as possible, and make sure your Tennessee address is solid and ready to be reviewed.