The 16-year-old centre-forward arrives following a successful trial at Brockhall last season in which he impressed in a 2-0 win over Manchester City.
Green will continue his Academy scholarship with Rovers through to June 2014 after which he will sign a two-year professional contract.
Academy manager Phil Cannon said: "Burton allowed Devarn to come on trial with us at the end of last season following a recommendation for our head of youth recruitment Alan Miller.
"He spent a couple of weeks with us, playing in a game against Manchester City and did really well.
"He's a quick striker with good technique. We think there is a lot of potential there."