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The 20-year-old striker has scored 16 goals this season and had been linked with a move to a number of clubs, including Manchester City and Celtic.
"It has been obvious over the last few weeks that John was keen to move sooner rather than later," said Rovers chairman Turnbull Hutton.
"Given that, we decided the time has come to maximise the financial return to Raith Rovers."
Raith had been holding out for a fee of £100,000 and had earlier rejected an offer for £35,000 from The Lions. Sutton may go straight into tomorrow's line-up but he is likely to make his debut a week on Saturday at home to Stoke City.