The 24-year-old signed a three-year contract with the League One club on Monday for an undisclosed fee, but The Star claims that Barnsley have made a profit on the defender and have inserted a sell-on clause in the deal.
Pearson joins Christoph Knasmullner in exiting Oakwell this summer, after the Austrian midfielder signed for Rapid Vienna earlier this month.
"Despite him being here just a short time, Matty [Pearson] was a great lad around the club and we feel this is a mutually beneficial move," chief executive Gauthier Ganaye told reporters.
"It was in our interests to get a good deal, which we certainly have done by making a profit on the player and also retaining an interest in his future.
"We've made the decision because Matty is wanting to play week in, week out this season, which we can understand and we were happy to satisfy that need."
Pearson made just 19 appearances for Barnsley last season after joining from Accrington Stanley last summer for £500,000.