The central defender, 17, had come through the Tykes' youth academy and was a regular in the reserve team at Oakwell last season.
Rovers boss Ronnie Moore told the club's official website: "Luke's a very talented young defender. He's big and strong, comfortable on the ball and knows how to tackle.
"He has a promising future ahead of him and I'm delighted to be able to bring him to Tranmere."