Hannahan, who played with a nagging back much of last season, is now eligible for free agency. Also, pitchers Rafael Perez and Chris Seddon were non-tendered after being designated for assignment earlier this week.
Hannahan made the Indians as a non-roster invitee in 2011 and started the past two seasons at third. He batted .244 with four homers and 29 RBIs in 105 games last season, a drop in his offensive production from 2011. He went on the disabled list in May with a calf strain and sore lower back.
The 32-year-old provided exceptional defence during his two seasons, but Chisenhall is viewed as the team's future at third.
After starting the season at Triple-A Columbus, Chisenhall batted .268 with five homers and 16 RBIs in 43 games. He broke his right forearm when he was hit by a pitch in June and was thought to be done for the year. But he came back and played in September, giving the Indians a chance to see him before they had to make a tough decision on the well-respected Hannahan.
The Indians tendered contracts to outfielder Shin-Soo Choo, closer Chris Perez, pitcher Justin Masterson, infielder Mike Aviles, catcher Lou Marson and relievers Tony Sipp and Joe Smith before Friday's midnight deadline.
Also, right-hander Corey Kluber, who is expected to compete for a starting job at spring training, underwent arthroscopic knee surgery at the Cleveland Clinic. The Indians said Kluber's knee locked up on him while he was playing with his young daughter at home in Jacksonville, Fla.
Kluber went 2-5 with a 5.14 ERA in 12 starts last season.
Earlier, the Indians and right-hander Blake Wood agreed to a $560,000, one-year contract -- a raise of $58,000 -- and avoided salary arbitration. Wood was claimed off waivers from Kansas City on Nov. 2. The 27-year-old had elbow ligament-replacement surgery in May and missed the entire season.
Cleveland has not gone to arbitration since 1991.