Guerrero had a bounce-back season, hitting .300 with 29 homers and 115 RBIs in 152 games in his first season in Texas. He hit .306 with 106 RBIs as the DH to lead all players in that role.
He becomes the second Ranger to win the award after Rafael Palmeiro in 1999.
It's not clear if Guerrero will be back with the Rangers next season. The team declined a $9 million option for 2011 on Guerrero's contract. He received a $1 million buyout, but the team has expressed interest in working out a new deal.
The designated hitter award is voted on by club beat writers, broadcasters and American League public relations departments. An outstanding DH has been named since 1973, and in 2004 commissioner Bud Selig named it after Martinez, a five-time winner.
Guerrero's award follows Rangers slugger Josh Hamilton who was named AL MVP on Tuesday.
Information from The Associated Press was used in this report.