Castledine, 20, has signed a four-and-a-half year contract with Boro, having impressed on loan in League One with Huddersfield Town this season. He moves to the Riverside for £1m.
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"I'm absolutely over the moon to join what is a massive, massive club," Castledine said.
"It's a really big step for me in my career and I'm very excited to be here.
"There's always been trust in young players at this club if they can perform, and I want to perform at my highest level."