A Twitter message from her staff said, "Wheels down Tucson. Gabrielle & Mark looking forward to a beautiful weekend."
The congresswoman will be spending the Fathers Day weekend with her family in Arizona, said spokesman C.J. Karamargin.
Giffords' husband, astronaut Mark Kelly, said she misses Tucson very much, and it will be a very emotional visit. She was released from a Houston hospital on Wednesday. Kelly spoke about that, outside the couple's Houston home.
"She wanted to leave, but she was a little bit apprehensive, a little bit of a sad day but she was happy to get here," said Kelly.
Giffords' doctors believe her return to Tucson could play an important role in her recovery.
She has left Houston twice since she arrived there in January, first in late April for Kelly's space shuttle launch. When the launch was scrubbed for mechanical reasons, she returned to Florida again for the successful May 16 launch.
Giffords is now living in Kelly's home in League City, 26 miles south of Houston. She will continue outpatient therapy at the same hospital where she underwent rehabilitation.
Giffords, who was shot in the left side of her head and has been struggling to relearn how to speak and walk, will be assisted by a 24-hour home health provider, according to a statement from the hospital.
Meanwhile, a judge has again denied a request by lawyers for shooting suspect Jared Loughner to be given notice before their client is given anti-psychotic drugs.
Loughner has been at a Missouri prison facility since May 28 after a judge declared him mentally incompetent to stand trial.
Loughner has pleaded not guilty to 49 charges stemming from the Jan. 8 attack.
The Associated Press contributed to this report.
