Rossi was born in Rome to a well-to-do family and lived his entire life in the city of his birth. He was educated by the Jesuits at the Collegio Romano, where he was a pupil of Bernardino Stefonio, Orazio Torsellino and Francesco Benci, the latter a student of the French humanist Muretus, one of the greatest Latinists of the Renaissance. Rossi soon distinguishing himself by his extraordinary command of Latin. At the age of 19 he received his laurea in jurisprudence at La Sapienza and in 1603 became a member of the Accademia degli Umoristi. The subsequent misfortunes of his family forced him to enter the legal profession. He remained in a precarious financial position until he received an appointment as secretary to Cardinal Andrea Baroni Peretti Montalto in 1610. After the cardinal's death in 1628 Rossi retired to a small house on the Gianicolo in Rome which became the centre for a circle of his fellow intellectuals including Alessandro Tassoni, Giovanni Ciampoli, Leone Allacci, Gabriel Naudé, and Fabio Chigi (the future Pope Alexander VII, whom Rossi called "Tyrrhenus). The image of Rossi that emerges from writings about him and from his own works is that of a cultured man, a meticulous philologist, and a tolerant thinker. His principal work, Pinacotheca Imaginum Illustrium containing three hundred short biographies of his contemporaries, both men and women, was one of the earliest examples of an Italian literary history, a genre which was to be developed in the 18th century by Ludovico Muratori and Girolamo Tiraboschi.