The 21-year-old joined Arsenal from Southampton in 2014 but has failed to establish a regular first-team place. He has won three England caps.
"Calum was the player we were waiting for and he's going to help us a lot," Middlesbrough manager Aitor Karanka said in a statement.
Chambers was named last week in the England Under-21 squad to face Norway in next month's Euro 2017 qualifier.
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(Reporting by Mark Greaves; Editing by Tony Jimenez)
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