The fee beats their previous record of £125,000, paid to Bristol City just last month for striker Paul Hefferman.
22-year-old Thornton played a significant role in the Black Cats' promotion to the Premiership last season, but has been deemed surplus to requirements at the Stadium of Light.
Rovers chairman John Ryan says the move, coupled with the recent capture of defender Phil McGuire from Aberdeen, is proof of his side's determination to win promotion this season.
He said: "This shows our determination to go for it this season by making this the best squad that Rovers have ever had.
"Sean and Phil are the type of quality players we are looking to bring in, and they won't be the last."