"I have more work to do on my recovery, so to do what is best for Arizona, I will step down this week," Giffords said in a video message to her constituents.
The Arizona Democrat was seriously wounded on the left side of her brain Jan. 8, 2011, when a gunman opened fire at her meet-and-greet "Congress on Your Corner" event outside a northwest Tucson supermarket. Six people were killed and 13, including Giffords were wounded.
"We know it is with the best interests of her constituents in mind that Gabby has made the tough decision to step down from Congress," President Barack Obama said in a statement.
"Over the last year, Gabby and her husband Mark have taught us the true meaning of hope in the face of despair, determination in the face of incredible odds, and now -- even after she's come so far -- Gabby shows us what it means to be selfless as well," Obama said, adding, "I'm confident that we haven't seen the last of this extraordinary American."
Giffords, 41, who has made significant progress in regaining her speech and motor skills, said she would continue her public service and plans to finish her event "that was interrupted by a gunman." Giffords plans to meet privately with several people who were there.
"I will return and we will work together for Arizona and this great country," she said in the 2-minute video on her Web site. "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. Jobs, border security, veterans. We can do so much more by working together."
Shooting suspect Jared Lee Loughner is undergoing psychiatric treatment at a federal facility in Missouri.
The Web site posting said Giffords would submit her resignation to U.S. House Speaker John Boehner of Ohio and Arizona Gov. Jan Brewer this week. Brewer will schedule a special primary and general election in Arizona's 8th Congressional District to fill the remainder of Giffords' two-year term.
"I don't remember much from that horrible day, but I will never forget the trust you placed in me to be your voice," Giffords said.