In a YouTube video to supporters, the Arizona congresswoman, a Democrat, said: "I have more work to do on my recovery, so to do what is best for Arizona, I will step down this week."
Giffords was left fighting for her life after a gunman shot her through the front of the head in an apparent assassination attempt, before spraying the crowd with bullets at her meeting with constituents outside a Tucson supermarket.
Among the six dead in the January 8, 2011 rampage were a federal judge, a nine-year-old girl and a member of the congresswoman's staff.
Giffords, whose speech remains halting and slurred, said in the video: "I don't remember much from that horrible day, but I will never forget the trust you placed in me to be your voice. Thank you for your prayers, and for giving me time to recover.
"I'm getting better every day. My spirit is high. I will return and we will work together for Arizona and this great country."
On January 8, Giffords made an emotional return to Tucson to mark the anniversary of the shooting, appearing at an outdoor stage at the University of Arizona, one of her rare public appearances since the shooting.
With her astronaut husband Mark Kelly nearby, she led the crowd in reciting the Pledge of Allegiance.
Giffords made a dramatic return to the House of Representatives last August to vote on a controversial debt compromise, drawing a standing ovation from Democratic and Republican lawmakers.
But the 41-year-old Giffords, who has spent much of the last year in Houston undergoing physical and speech therapy, has been faced with a tough decision on whether to campaign for another two-year term. Since the shooting, she has cast just one vote in Congress, on the debt ceiling.
She gave a televised interview to ABC but otherwise has remained out of public view.
In her two-minute video, Giffords says: "A lot has happened over the past year. We cannot change that. But I know on the issues we fought for, we can change things for the better."
In March, the alleged shooter, Jared Loughner, was declared mentally unfit to stand trial. Experts found the 23-year-old to be schizophrenic and unable to help in his own defense or understand court proceedings.
Soul-searching in the aftermath of the tragedy focused on the toxic political climate in the United States and whether it in some way inspired the misfit gunman.
Giffords said in a statement she will submit her letter of resignation later this week to House Speaker John Boehner and Arizona Governor Jan Brewer, who will set dates for special primary and general elections to determine who will serve the remainder of her term.
Democratic House leader Nancy Pelosi said: "Gabby has been an inspiring symbol of determination and courage to millions of Americans" and added that "Gabby's message of bipartisanship and civility is one that all in Washington and the nation should honor and emulate. "
Boehner said in a tweet, "We salute Rep. Giffords for her service, & for the courage & perseverance she has shown in the face of tragedy. She will be missed."
Before she leaves office, Giffords will finish her "Congress On Your Corner" event that was halted by the shooting spree. She said she will meet privately with some of the people who were at that event.
As one of her last acts as a member of Congress, Giffords will attend the State of the Union speech Tuesday at the Capitol.