Monk, who quit Leeds last month, has beaten one-time Boro player Nigel Pearson to the job after both men were interviewed by chairman Steve Gibson.
Monk was also approached by Middlesbrough’s also-relegated, equally-managerless neighbours Sunderland .
But, with no appointment imminent at the Stadium of Light following David Moyes’ resignation, the Teessiders stole a march on their rivals.
He replaces Aitor Karanka, who was sacked in March as Boro tried in vain to avoid an instant return to the Championship.
Monk will be given cash to mount a promotion campaign.