Giffords landed at Houston's Hobby Airport shortly after 1 p.m. CST and immediately was transported to TIRR Memorial-Hermann Hospital via medical helicopter. She is now in the hospital's ICU, surrounded by her family.
Before departing for Houston yesterday morning, Giffords left the Tucson hospital where she had been treated since suffering a gunshot to her head in an attack nearly two weeks ago. She was the last shooting victim to leave the hospital.
Cheered by crowds of well-wishers, Giffords was taken by ambulance to a nearby Air Force base where a specially equipped private plane was ready to carry her to Texas.
Giffords was accompanied to Houston by her astronaut husband, Capt. Mark Kelly, her doctors, and her mother, Gloria Giffords.
Along her roughly 10-mile route to the Air Force base, crowds of supporters stood on the curb, cheering and waving flags and signs as her motorcade passed by. Giffords' ambulance was escorted by a squadron of military veterans on motorcycles.
"We could hear applause in the ambulance with Gabby, and she responded very well to that, smiling and even tearing a little bit," said Dr. Randall Friese, one of the doctors who treated Giffords in Tucson. "It was very emotional and very special."
At a press conference in Houston late yesterday afternoon, Giffords' medical team said yesterday's trip went flawlessly and that while she has a long road ahead, she has great potential for rehabilitation.
Now that her Tucson team has handed over responsibility for Giffords' care, they said their goodbyes and will return to Arizona.
"I'm going to miss her a lot," said Tracy Culbert, the nurse who cared for Giffords over the last two weeks in Tucson and accompanied her on the plane. "She's a very gentle person, and her personality is coming out with touches. ... I'm very lucky to know her."
Giffords' husband, Kelly, who lives in Houston, said Thursday that the congresswoman 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 another sign of progress, Giffords was taken outside Thursday for the first time since the attack to give her 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 the actions described by her doctors as "fantastic achievements forward."
The motive behind the attack that killed six people and wounded 14 might never be understood, Kelly said.
"I don't think we're ever going to fully understand the why and the how and the reason for what happened on the eighth of January," he said. "This has been a challenge for all of us.
"But what it has done is that it's certainly shown me, and not only our country but the entire world, what Tucson is all about," he added. "I know my wife Gabrielle would be very proud of how this community has responded to this tragic situation."
Kelly also joked that he knows Giffords can't wait to write "thank you" notes to all of her supporters.
The Associated Press contributed to this report.