Gaudette was born in Manchester, New Hampshire on 25 March 1902. On 12 August 1925, as a young adult, she became a nun. She lived in Canada and France, teaching music and art for many years.
Gaudette voted for Dwight D. Eisenhower in the 1952 U.S. presidential election, and moved to Rome in 1958, living in a convent there for the rest of her life. She retained U.S. citizenship, and was proud to be an American.
In 2008, after a 56-year hiatus, Gaudette cast her ballot in the U.S. presidential election, voting for Barack Obama. At the time, aside from her declining hearing, she was still in good shape, being able to watch the television and read newspapers. At the age of 110, she could still use a typewriter.
At the age of 114, Gaudette became the oldest American-born person and U.S. citizen after the 12 May 2016 death of Susannah Mushatt Jones. Later that year, she surpassed the age of Eugénie Blanchard to become the oldest nun ever, and later became the first nun to reach the age of 115. Her niece and great-nephew flew from the U.S. to celebrate the occasion. In April 2017, she became the oldest resident of Italy following the death of Emma Morano.
Gaudette died on 13 July 2017 at the age of 115 years, 110 days. She had been a nun for 92 years. The oldest living person in Italy after her death was Giuseppina Projetto, and Lucile Randon (Sœur André) became the oldest living nun. She remains the oldest person ever born in the U.S. state of New Hampshire.