The 23-year-old, a graduate of the FC academy, has been informed that his deal will not be renewed by the Black and Whites.
He has been playing for Doncaster on a dual-registration deal, but has now opted to join Rovers with a view to earning a deal somewhere.
“He came through our ranks here and is a good professional, but his chances in the first-team here have been limited.
“We have decided not to renew Liam’s contract at the end of the season, so the move presents a good chance for him to earn a new deal and continue his career elsewhere.”
Kent will play under former FC coach Andy Hay for Rovers.