The hostage, who was "abducted last year in Yemen, arrived overnight at Doha airport after having been freed thanks to mediation by Qatar," said the agency, without elaborating.
Gunmen abducted the woman on March 14, 2012 from her home in Hodeida, western Yemen, where she had been working there as a language teacher.
Her abductors took her to the southeastern province of Shabwa where Al-Qaeda has a strong presence.
A Yemeni interior ministry spokesman said the kidnappers had called on the Sanaa government to free members of their tribe in exchange for her release.
Switzerland confirmed the woman was free and had arrived in Doha, with ATS news agency saying that Foreign Minister Didier Burkhalter had already spoken to her by telephone.
She was in good health, and was poised to return to her homeland, ATS reported.
The ministry hailed Qatar's role in freeing the 33-year-old woman, but gave no further details.
QNA quoted Qatar's assistant foreign minister Ali bin Fahd al-Hajiri as saying: "I take this opportunity to thank the Qatari negotiating team who has been working during the past few months silently, and with wisdom and patience until we got to this positive outcome."
In a video posted on the Internet in May last year, the woman had said she was in the hands of Al-Qaeda, while in a second video, she implored Switzerland to help free her.
Most kidnappings of foreigners in the impoverished Arabian Peninsula state are carried out by members of the country's powerful tribes who use them as bargaining chips in disputes with the central government.
Less frequently, Al-Qaeda militants carry out such kidnappings.
Yemeni authorities are still trying to free two Finns and an Austrian snatched from central Sanaa late last year.
The Austrian man and Finnish man and woman were abducted on December 21st as they prepared to travel to the southern port of Aden via Yemen's second city Taez.
Yemeni security officials had said the three were being held by Al-Qaeda-linked tribesmen in the eastern province of Marib.
Here's the video from May 2012: