The goalkeeper will move to the Riverside to compete with Victor Valdes for the number one spot.
Guzan has been with Villa since leaving his native USA in 2008, but has fallen out of favour at the club and will now be granted a free transfer.
He lost his place to understudy Mark Bunn during the latter stages of last season, and with the arrival of young highly-rated Italian stopper Pierluigi Gollini this summer his days at Villa Park have appeared numbered.
For Villa, the deal makes sense; Guzan would be unlikely to command too high a fee, and by waiving that and allowing him to leave for free, the club will be able to shift another high earner off their books.
Villa have already released Charles N'Zogbia and Kieran Richardson this summer as they look to trim down their wage bill and look to the future.
From Middlesbrough's perspective, however, the move is perhaps a slightly peculiar one.
Boro have already signed Valdes this summer and the former Barcelona man will surely be number one. Meanwhile, last season's number one, veteran stopper Dimi Konstantopoulos, and his deputy Tomas Mejias remain on the books.
The arrival of Guzan seems to suggest that at least one of those pair will be departing over the next few weeks, as Guzan will surely serve as understudy to Valdes.