The deal includes a $3.25 million option for 2014 with a $150,000 buyout.
General manager Jeff Luhnow made the official announcement Friday.
According to Ken Rosenthal of FOX Sports, Houston intends to utilize Veras as the club's closer in 2013.
Veras, 32, posted a 5-4 record with a 3.63 ERA and 79 strikeouts over 67 innings in 72 appearances for the Milwaukee Brewers last season.
He's established himself as one of the most dependable relievers in the majors, as evident with making 151 outings over the previous two seasons with the Brewers and Pittsburgh Pirates.
This mark places Veras tied for second among all pitchers in that span.
Veras is 19-17 with a 4.01 ERA and 328 strikeouts over 314 1/3 innings in 327 relief appearances over seven career major league seasons with the New York Yankees (2006-09), Cleveland Indians (2009), Florida Marlins (2010), Pirates (2011) and Brewers (2012).
With the signing of Veras, the Astros will make a corresponding roster move to the 40-man roster at a later date.