She and her husband, retired astronaut Mark Kelly, bought a home in Tucson and moved in over the weekend.
"You know, it's time for her to get back to as much of a normal life as possible after this type of catastrophic injury," Kelly told an Arizona newspaper. "Obviously, a big thing for her is to come home."
Giffords had been in Texas for months undergoing intensive physical and speech therapy after she was wounded in a mass shooting in January 2011. Kelly said Giffords will continue to undergo therapy in Tuscon at a reduced pace.
"It was very important for her to be in Houston, where she was able to get very specific therapy for this type of injury," Kelly said. "She did that for a year and a half, and the second we realized that was going to start winding down, it was time for us to start looking forward to how we could get to Tucson."
Six people died in the shooting and Giffords is one of 12 survivors. Jared Loughner, the suspected gunman, pleaded guilty to that shooting last week. The plea helped him avoid a possible death penalty. His sentencing is set for Nov. 15.
The Associated Press contributed to this report.
