Excerpts from the videotapes will also be broadcast Monday on the ABC News program "20/20."
The Arizona Democrat has gone from not knowing who she was and why she was in a hospital to being able to walk and talk. She told Diane Sawyer she feels "pretty good."
But she said the recovery process has been "difficult, difficult."
Giffords left the rehab hospital for the first time in late April to watch the launch of the Space Shuttle Endeavour on its final mission with her husband in command. In August, she returned to the House for the first time for the vote on raising the debt ceiling.
Kelly told Sawyer he made the videos because he was convinced Giffords would recover and would have a lot of questions about what happened to her.
Giffords' accused shooter, Jared Loughner, has been found unfit to stand trial. He is being held in a federal prison hospital in Missouri.