An ambulance transported her just after 8:30 a.m. Central Standard Time. Helicopters buzzed overhead and there was a heavy police presence. A shot from a news helicopter showed a gurney wheeled into the building.
The move came after doctors upgraded her condition from serious to good.
Doctors said she can still breathe on her own, her speech function is improving and she's becoming more interactive. A tube that was draining excess fluid from around Giffords' brain was removed. Doctors also plan on inserting a speaking valve into her breathing tube to help her talk.
Giffords was critically wounded in the Tucson mass shooting that killed six people and injured 12 others on Jan. 8.
Giffords had been kept in intensive care since her arrival Friday at the Houston hospital from Tucson, Ariz.
Doctors at Memorial Hermann Texas Medical Center Hospital determined that she was ready to move to TIRR Memorial Hermann, where her rehabilitation will begin. That transfer is pending a review of her condition.
During Tuesday's State of the Union address, many lawmakers in both parties wore black-and-white lapel ribbons to signify the deaths and the hopes of the survivors. A chair was left empty in Giffords' honor.
The same ribbon was also worn by Giffords' husband, Mark Kelly, as he watched the speech from his wife's hospital bed more than 2,000 miles away. Although he was likely invited, Kelly chose not to attend the event.
"We're also mindful of the empty chair in this chamber and we pray for the health of our colleague and our friend Gabby Giffords," /*President Barack Obama*/ said.
Meanwhile, the 22-year-old suspect in the shootings, /*Jared Loughner*/, pleaded not guilty Monday to federal charges of trying to assassinate the congresswoman and two of her aides.
The Associated Press contributed to this report.
