Other winners were: Tampa Bay first baseman Carlos Pena; Boston second baseman Dustin Pedroia; Texas shortstop Michael Young; New York Yankees pitcher Mike Mussina; and Minnesota catcher Joe Mauer.
"I take a lot of pride in my defense," Hunter told MLB.com. "It's one part of the game that can be a constant if you concentrate on what you're doing."
Hunter joined the LA Angels in 2008 following seven seasons with Minnesota.
Mussina won his seventh Gold Glove, but his first since 2003, and Mauer was a first-time winner.
NL winners were announced Wednesday.
The 2008 season marked the GGA's 52nd year.