Paganini earned an electrical engineering degree and a licenciate in mathematics in 1990 from the University of the Republic (Uruguay).
He came to the California Institute of Technology for graduate study in electrical engineering, earning a master's degree in 1992 and completing his Ph.D. in 1996.
After postdoctoral research at the Massachusetts Institute of Technology he became an assistant professor at the University of California, Los Angeles in 1997, earned tenure there, and remained there as a faculty member until 2005, when he returned to Uruguay as a professor at Universidad ORT Uruguay.
[2] In April 2020, Paganini was appointed a member of the GACH, an advisory committee created by President Luis Lacalle Pou to define methods and studies to advise the government regarding the COVID-19 pandemic in Uruguay.
[3] With Geir E. Dullerud, Paganini is a coauthor of the book A Course in Robust Control Theory: A Convex Approach (Texts in Applied Mathematics 36, Springer, 2005).