Although the Northern Ireland striker was out-of-contract at the Potters, as he was under 24 they are entitled to a fee for his development.
They will receive £275,000 up front, with appearance-related fees meaning they are set to receive a total of £425,000 from the Iron.
"We are very disappointed with the verdict, as it falls well short of our valuation of him," said Stoke director of football John Rudge.
"We had Martin at the club since he was nine-years-old, and played a significant role in helping him become the player he is today.
"This season he is one of the top scorers in the Championship, so to receive the verdict we have is very disappointing."
Stoke will also get 20 per cent of any future transfer fee Scunthorpe receive for Paterson plus a further £250,000 in the unlikely event of the Iron winning promotion to the Premier League in the next two seasons.
But the Potters were asking for a whopping £750,00 up front plus appearance annd goal clauses, and a sell-on fee.
Since arriving at Glanford Park Paterson has broken into the senior Northern Ireland side, making his international debut in a Euro 2008 qualifier against Spain.