The 38-year-old former Swansea and Leeds boss will be unveiled at a press conference on Monday after agreeing to take over as Aitor Karanka's replacement.
The club said in a statement: "Middlesbrough FC are delighted to confirm the appointment of Garry Monk as the club's new manager. Garry will be officially unveiled at a media conference on Monday."
Boro are yet to confirm the length of Monk's contract, while the wording of their announcement - that he is "manager" rather than "head coach", as Karanka was - may well be significant.
Monk was one of a series of potential candidates to whom chairman Steve Gibson spoke, including Karanka's assistant Steve Agnew, who took charge for the final 11 games of last season, before making his choice.
He was available after parting company with Leeds last month after guiding the Elland Road club to the fringes of the Sky Bet Championship play-offs, only for the two parties to fail to reach agreement over an extension.
Monk's remit will be to guide Boro into the Premier League after their first season back in the top flight ended in a heart-breaking relegation following a seven-year quest to return to the promised land.
Karanka left the Riverside Stadium in March with Boro deep in relegation trouble, and Agnew was handed the task of halting an alarming slide.
However, he was unable to do so and, in the process, any chance of landing the job on a permanent basis dissipated.
Monk will at least have the core of the squad which won promotion two seasons ago at his disposal, and with Gibson having vowed to "smash" the Championship this time around, there could be money to spend too.
However, there will also be a clear-out to be managed - Victor Valdes and Brad Guzan have already left, while loan signings Calum Chambers and Alvaro Negredo have returned to their parent clubs - with several players having spoken openly of dressing room unrest in the wake of relegation.
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