Guzan had one year remaining on his contract, but has reportedly been allowed to leave on a free transfer.
The 31-year-old made 170 appearances for Villa after joining from American side Chivas USA in August 2008.
He is the second keeper to join Boro this summer, following the arrival of former Manchester United and Barcelona man Victor Valdes.
Find all the latest football transfers on our dedicated page.
Premier League newcomers Middlesbrough have signed Aston Villa goalkeeper Brad Guzan on a two-year deal.