Described as a 'diligent fantasy maker', Rossi was one of the rare performer-composers of the 17th century.  Born in Genoa, he was a virtuoso violinist as well as an organist and composer.  At that time, performer-composers were judged more by their performing ability, which may explain why Rossi’s printed keyboard output is so scarce.  His entire printed keyboard output consists of only one volume of toccatas and correntes.  Rossi began keyboard study with his uncle, Lelio Rossi at the Cathedral of the San Lorenzo in Genoa.  His only other noted influence was Johann Froberger.  Rossi is thought to have taken lessons from Froberger in the years 1637-1640, but there is no direct proof of their meeting.  The stylistic characteristics of Rossi's music however, gives us reason to assume that they were at least acquaintanted with one another.

The years that Rossi spent in Rome are his most important and influential in terms of musical output.  The ten-year period from 1624-1634 encompasses Rossi’s service at Cardinal Maurizio di Savoia’s court, his position as organist at St. Luigi dei Francesi, as well as the composition and production of his opera Erminia sul Giordano in 1633. 

From 1634-1638, Rossi was in the service of Francesco I d’Este in Modena.  During this time, his opera Erminia was published in Rome in 1637 and his new opera, L’Andromeda was first performed in Ferrara in 1638.

After 1639, there is little information regarding Rossi’s location or compositions until 1649.  This ten-year period marks a void of information.

In 1649, Rossi returned to Rome and became a resident at the Pamphili palace (Pope Innocent X), until 1655.  

Rossi lived during the time of two different Popes, Urban VIII (a Barberini) from 1623-1644 and Innocent X (a Pamphili) from 1644-1655. Urban VIII was the last Pope to expand the papal territory by force of arms, and was a prominent patron of the arts and reformer of Church missions. However, the massive debts incurred during his papacy greatly weakened his successors, who were unable to maintain the Pope's longstanding political or military influence in Europe.  Soon after Innocent X’s accession, a legal action against the Barberini for misappropriation of public funds was initiated.  Their property was confiscated and the family fled to France.  Later, the Barberini were rehabilitated.     

When Rossi died in 1656, his excellence as a violinist was so widely recognised that it was noted in the register of his death.