Doctors at Memorial Hermann Texas Medical Center Hospital determined the congresswoman was ready to move Wednesday morning to nearby TIRR Memorial Hermann, where her rehabilitation will begin.
An ambulance transported her a short way just after 8:30 a.m. Central Standard Time. Helicopters buzzed overhead and there was a heavy policy presence. A shot from a news helicopter showed a gurney wheeled into the building.
Giffords' husband, astronaut Mark Kelly, rode in the passenger's seat of the ambulance with his arm rested on the open window.
Giffords had been in intensive care since her arrival Friday from Tucson, Ariz.
Doctors in Texas said she had been given a tube to drain excess cerebrospinal fluid.
Everyone makes such fluid, but an injury can cause the fluid to not be cleared away as rapidly as normal. A backup can cause pressure and swelling within the brain.
Giffords was shot in the head Jan. 8 in a rampage that killed six people and injured her and 12 others. The three-term Democratic congresswoman was hit in the forehead while meeting with constituents outside a Tucson supermarket.
The assassination attempt cast a somber mood over President Barack Obama's State of the Union speech on Tuesday night, where many lawmakers in both parties wore black-and-white lapel ribbons to signify the deaths and the hopes of the survivors. Giffords' husband, astronaut Mark Kelly, watched the speech from her bedside in Texas, as he held her hand.
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. He also faces federal murder charges in the deaths of a federal judge and a Giffords aide, and more charges were expected.
