The 17-year-old had been courted by a number of Premier League teams - including his former side Everton - after impressing this season with his performances for Rovers' Under-23s side, who are challenging for promotion from the Premier League 2's division two.
Rovers' Academy manager Stuart Jones said of the deal: "Ultimately, we did everything we could to try and keep Callum, but the situation was taken out of our hands when Premier League clubs became interested.
"He's a young player and when Premier League clubs came calling both he and his family were keen to move on.
"I think it reflects well on the quality and standard of players we're producing at the Academy, and we will continue to develop players for the first team and work hard to keep them at this football club, because this is the ideal environment for young players to develop and progress."
Wright moved to Rovers from the Toffees' youth setup in 2016.