Loughner's plea allows him to avoid the death penalty.
Federal Judge Larry A. Burns had found that Loughner was mentally unfit to stand trial. He ruled on Tuesday that months of forcibly medicating him to treat his schizophrenia made him competent to understand the gravity of the charges against him and assist in his own defense.
Loughner is expected to be sentenced to life in prison without parole.
Loughner had previously pleaded not guilty to 49 federal charges stemming from the Jan. 8, 2011, shooting outside a supermarket where Giffords was holding a meet-and-greet with constituents. Authorities said Loughner shot Giffords in the head, then turned his gun at the crowd before being subdued by bystanders. Giffords subsequently left Congress to devote her time to rehabilitation.
The Associated Press contributed to this report.