The 22-year-old suspect, Jared Loughner, is being held in federal custody.
Giffords has been making progress each day during her stay at University Medical Center in Tucson. Her husband, astronaut Mark Kelly, tweeted Friday: "GG going to next phase of her recover today. Very grateful to the docs and nurses at UMC, Tucson PD, Sheriffs Dept....Back in Tucson ASAP!"
Doctors said Giffords' transfer went smoothly. She left the hospital in an ambulance. She then took a plane to the Houston airport and a helicopter took her to the ICU at Texas Medical Center, where she'll be evaluated before going to the center's rehabilitation hospital, TIRR Memorial Hermann.
Despite her progress, doctors warn Giffords has a long road to recovery. They are not sure what, if any, disability she will have. She is moving both arms and legs, but it's unclear how much strength she has on her right side, since the bullet struck the left side of her brain.
Giffords will stay at the Houston rehabilitation center until she no longer needs 24-hour medical care, which on average takes one to two months.
The Associated Press contributed to this report.
