At a press conference in Houston late Friday afternoon, Giffords' medical team said that the trip went flawlessly and that while she has a long road ahead, she has great potential for rehabilitation.
Giffords' husband, Kelly, who lives in Houston, said last Thursday that she soon would be "back at work" and predicted she would be walking around in a couple of weeks.
"I'm extremely hopeful that Gabby will make a full recovery," he said. "She is a fighter like nobody else I know."
In other signs of progress, Giffords was taken outside Thursday for the first time since the attack so she could get some sunlight. She stood up Wednesday for the first time with assistance and looked out of a hospital window.
Giffords already has been able to scroll through an iPad, one of many steps described by her doctors as "fantastic achievements forward."
The Associated Press contributed to this report.