Thompson, pictured, left Westfield Lane on Monday afternoon after the Blues announced they'd agreed a deal for an undisclosed fee which also includes a substantial sell-on clause.
The 21-year-old joined Frickley in mid-October last year from Retford United, impressing with 16 goals in 32 appearances, including two in the Sheffield & Hallamshire Senior Cup Final in May.
Thompson has attracted interest from several clubs since the start of pre-season with York and another Football League club both bidding for his services. Both had offers accepted over the weekend with the striker opting for a switch to Bootham Crescent.
Frickley Athletic chairman Gareth Dando said: “We’ve had a lot of interest in Reece and a number of offers for the player over the past few weeks.
"We got to a situation last week where we received offers from two clubs which matched our valuation of the player and the decision was then up to Reece. We wish him well at York and are sure he’ll be a success there.”
He added: "All the management and officials of Frickley Athletic thank Reece for his efforts while at Frickley and wish him all the best in his professional career."
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