Giffords, 42, and her husband, retired astronaut Mark Kelly, were to leave Houston Monday for Tucson, where they recently purchased a home, the Arizona Daily Star reported.
"She's gone home before to visit, but this is different," Kelly said Saturday. "She'll be home for good. She's very, very happy."
Giffords has been living in Houston, her husband's home, since Jan. 21, 2011, so she could receive specialized help recovering from an assassination attempt Jan. 8, 2011.
Six people died and 13 people, including Giffords, were wounded during a "Congress On Your Corner" event with constituents in front of a Tucson grocery store.
In Houston, Giffords underwent rehabilitation as an inpatient then as an outpatient at the Texas Institute for Rehabilitation and Research Memorial Hermann Hospital.
"[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."
Giffords resigned her congressional seat Jan. 25, saying she needed to focus on her recovery.
Kelly said Giffords' therapy regime in Tucson wouldn't be as intense as in Houston.
"She's getting to the point with some things she needs less than others. 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 said. "Obviously, a big thing for her is to come home."