Generally yes, particularly if there is a supervised release component to the sentence.
When parole or probation is part of the release, the supervising jurisdiction is almost always the county where the conviction occurred. That is where the case originated, where the judge issued the sentence, and where the probation or parole office has jurisdiction over the case. Your inmate will typically be required to report to that county's supervision office and establish themselves there as the starting point of their reentry.
Moving to a different county or state is possible but not automatic. It requires a formal transfer request that has to be approved by both the originating county and the receiving jurisdiction. The bar for approval is specific and practical. The person needs to demonstrate three things clearly: a confirmed job or legitimate employment prospects, verified stable housing at the proposed new address, and a record and attitude that suggest they are a good candidate for the transfer rather than someone trying to dodge supervision.
Without all three of those elements in place, a transfer request is unlikely to be approved. A general preference to live somewhere else is not sufficient. The system wants to see that the transfer serves the goal of successful reintegration rather than just convenience.
If release without supervision is the situation, meaning the sentence is fully completed with no parole or probation to follow, your inmate can generally go wherever they choose. Gate money and a bus ticket take them to an approved release address, but without a supervising officer there is no legal requirement to stay in the originating county.
Have him talk to his case manager about the specific conditions of his release well before the out date so there are no surprises.