Mapelli, a professor of psychology, will assume the position on Friday, beginning her six-year term in time for the Italian university’s 800th anniversary next year.
The 55-year-old hails from the Lombard city of Lecco and is a mother of two.
She was vying for the position alongside another woman, law professor Patrizia Marzaro.
Making reference to the rows of portraits of past rectors – eight centuries of male faces – Mapelli said: “Now more than ever before, the portraits of these men seem to vividly convey to me their stories, thoughts and hopes.”
“Who knows if at the moment of their election they were moved, as I am now,” she added.
“From October, we will finally be able to say: ‘Men and women who led the University of Padua’.”
The election of Mapelli comes a year after Rome’s Sapienza University appointed Antonella Polimeni as its first rector since the university was founded by Pope Boniface VIII in 1303.
Padua is the second-oldest university in Italy, after Bologna, and the fifth-oldest surviving university in the world.
Copernicus and Galileo studied and taught at the university, and in 1678 Venetian student Elena Lucrezia Cornaro Piscopia became the first woman to graduate there, with a degree in philosophy.