She earned a master's degree in mathematics in 1984 at the University of Rome La Sapienza, and a PhD in 1989 at the Swiss Federal Institute of Technology in Zurich (ETH) under the supervision of Jürgen Moser and Jörg Waldvogel.
[3] In 2015 she was elected vice-President and in 2018 became President of the Scientific Committee in Celestial Mechanics of the International Astronomical Union.
Since April 2020 she is member of the Governing Board and Vice-President of “ANVUR - Italian National Agency for the Evaluation of Universities and Research Institutes”.
In 2007, her book Ordine e caos nel sistema solare in collaboration with Ettore Perozzi was a finalist for the Galileo Popular Science Prize.
In 2023, Alessandra Celletti won the Brouwer Career Award from the Division on Dynamical Astronomy of the American Astronomical Society.