She expects to attend the president's State of the Union address on Tuesday.
Arizona Gov. Jan Brewer (R) announced that she would call a special election to fill the seat.
Giffords suffered a bullet wound to her head when a gunman opened fire at a constituent event in Tucson, Ariz. Jan 8, 2011.
Since the shooting, Giffords has regained the ability to walk and speak and doctors have praised her recovery as a miracle.
On the one year anniversary of her shooting, Obama spoke with Giffords and praised her "courage and determination." The president told the three-term congresswoman that he and the first lady still mourn the victims of the shooting rampage will claimed six lives and wounded 13 people including Giffords.
In his statement on Sunday, the president said Giffords's "cheerful presence will be missed in Washington."