Giffords said she wants to focus on recovering from wounds suffered in an assassination attempt outside a Tucson, Ariz., supermarket last January.
Washington officials expect her resignation to take effect Monday.
In a two-minute video posted to her Facebook page, Giffords said: "I don't remember much from that horrible day, but I will never forget the trust you placed in me to be your voice." She said, "I'm getting better. Every day my spirit is high. I will return and we will work together for Arizona and this great country."
While Giffords has appeared to have a remarkable recovery, she stated on Facebook that she still has more work to do and resigning her seat in the House would be beneficial.
A special election will be held in Arizona to fiil out the remainder of Gifford's term.
House Democratic leader Nancy Pelosi called Giffords "an inspiring symbol of determination and courage to millions of Americans."
The Associated Press contributed to this report.