This marks the third time in the last four seasons that the Yankees have had at least two Gold Glove winners in the same year. Derek Jeter and Teixeira also won in 2009, while Cano, Jeter and Teixeira all won in 2010.
In 2012, Teixeira led qualifying Major League first basemen with a career-best .999 fielding percentage, committing just one error in 1,055 total chances during the regular season.
It marked the best single season fielding percentage by any Major League first baseman over the last three seasons (2010-12) and the 11th best single-season mark at first base in the modern era (since 1900).
Teixeira's .999 fielding percentage also established the Yankees franchise record at his position, surpassing Don Mattingly's .998 in 1994 (two errors in 989 total chances).
"I am honored to accept the Gold Glove Award and appreciate the recognition for my defense," Teixeira said. "There are a lot of great first basemen in the American League and I will continue to work hard to stay on top of my game defensively."
Other Yankees first basemen to win the award are Joe Pepitone (1965-66, '69), Chris Chambliss (1978) and Mattingly (1985-89, '91-94).
Cano, who led all American League second basemen with 726 chances in 2012, finished second in the AL with a .992 fielding percentage while making just six errors.
He is just one of two Yankees second basemen to win a Gold Glove, along with Bobby Richardson, who won the honor in five straight seasons from 1961-65.
"It's another dream come true for me," Cano said. "The Gold Glove is a special award because my defense is something I take a lot of pride in. There are a lot of ways you can contribute to a team win. It's not always about offense. Sometimes saving runs is as important as scoring runs."
Each Major League manager and up to six coaches on each staff voted from a pool of qualified players in their respective league. Voters were not permitted to select players from their own team.
Yankees catcher Russell Martin was also nominated for a Gold Glove, but the award went to the Orioles' Matt Wieters. As a team in 2012, the Yankees' .987 fielding percentage ranked third in the Majors and their 74 errors were the third-fewest.