The 32-year old, reunited with former Cleveland teammate Shin-Soo Choo, hit .244 for the Indians last season with 16 doubles, four homers and 29 RBIs in 105 games. His playing time was limited by a minor back injury.
"It's a chance to win," Hannahan said during a news conference at Great American Ball Park. "I'll do whatever they ask me to do. If that's to play every day, if that's to come off the bench late and hit or play defense, I'm ready for everything."
Hannahan gets $1 million in each of the next two seasons, and the Reds have a $4 million option for 2015 with a $2 million buyout.
He became a free agent when the Indians failed to offer him a 2013 contract by the Nov. 30 deadline. In six big league seasons with Detroit, Oakland, Seattle and Cleveland, Hannahan has made 451 appearances at third base, 39 at first, nine at shortstop and one at second.
"I've bounced around positions throughout my career," he said.
Cincinnati has been busy this week, acquiring Choo and agreeing to a $15 million, two-year deal to keep outfielder Ryan Ludwick.
"Jack is known for being a great teammate and a clubhouse leader everywhere he's been," Reds general manager Walt Jocketty said. "He's very good defensively and is capable of playing any infield position. We think he was the best utility player out there."
Todd Frazier, who hit .273 with 18 homers and 67 RBIs and a rookie, is expected to be the starter at third. Cincinnati could have plenty of backup choices.
The Reds are awaiting a decision from Scott Rolen on whether he plans to play next year or retire. The 37-year-old hit .245 with eight homers and 39 RBIs in 92 games during an injury-filled season and is expected to make a decision within two weeks.
"He's been so important to our success the last couple years, and an instrumental part of our team and the clubhouse," Jocketty said. "If he wants to play, we have to see if we can work something out, to his satisfaction and ours."
Hannahan followed Choo and Jason Donald across Ohio from Cleveland.
"I'm a big fan of Choo," Hannahan said. "I love the way he plays the game. He shows up every day. He's as tough as they come. I think he'll do big things here.