"Our compatriot Isabelle Prime has been freed tonight," the statement read.
She is currently under French protection, the statement said, without giving further detail on when or where she would arrive back in the country.
There is no confirmation yet on the identity of her kidnappers.
The 30-year-old, who worked as a consultant on a World Bank-funded project, was seized with her translator Sherine Makkaoui as they were driving to work in the capital Sanaa. Makkaoui, who is Yemeni, was freed in March.
France has made "every effort to achieve this happy outcome", the statement said, adding that the presidency "expresses its gratitude to all those who worked on this solution, including Sultan Qaboos Bin Said, sultan of Oman".
President Francois Hollande "shares the joy of the family of Isabelle, who have demonstrated great courage and great responsibility during the long wait", it said.
Prime, originally from the west of France, arrived in Yemen in 2013.
In June she appeared in a 21-second video posted on YouTube by her captors.
Seated on the ground and dressed in black, she appealed to the French and Yemeni presidents to secure her release.
Francisco Ayala, president of Ayala Consulting, Prime's employer, told AFP late Thursday that he received news of her release through a telephone call from the French foreign ministry.
He said: "The whole thing was very secret. The government of France never told me or even her father anything (about efforts to secure her release). I guess more news will come later."
He said Prime could arrive in Paris as early as Friday.
Ayala, who spoke via Skype from his firm's base in Ecuador, said he had spoken to Prime's father, who Ayala said was planning to travel to Paris Friday.
Prior to Prime's release, the most recent French hostage to be freed was Serge Lazarevic in December last year, after he spent three years in the hands of Islamist militants in Mali.
At the time of his release, Lazarevic was the last of more than a dozen French citizens taken captive in recent years, with those held in Africa reaching a high of 15 last year.