The 22 year-old has signed an 18-month contract just a few days after arriving at Spotland on loan.
He made his Rochdale debut in Saturday's 4-0 FA Cup fourth-round defeat by Championship club Huddersfield Town.
Kitching joined Middlesbrough in July 2013 and played twice for Boro in the EFL Trophy earlier this season.
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League One Rochdale have signed on-loan defender Mark Kitching on a permanent deal from Middlesbrough.