The 21-year-old scored five goals in 15 appearances during a temporary stay at Chesterfield last season, and Town boss Mark Robins believes moving to Rovers will further help his progression.
"Chris enjoyed a similar loan in League Two with Chesterfield during the opening stages of last season and we believe the step up to League One will once again improve him further as a footballer.
"I have a good relationship with Ronnie Moore having played under him at Rotherham and I know that he will help develop Chris's skills.
"Competition for a midfield spot is strong and Chris needs first team football.
"Tranmere were pushing for promotion last season and we believe they will provide Chris with an excellent environment to play football in."