Tommaso Inghirami was born in Volterra in 1470, the son of Paolo Inghirami and his wife Lucrezia Barlettani. His father, a prominent man in Volterra, was killed in a political uprising in 1472. After the murder, Paolo's children were taken to Florence. Later, at a young age, Tommaso was sent to Rome to live under the protection of Bishop Jacopo Gherardi and Tommaso's uncle, Antonio Inghirami, a secretary to Pope Sixtus IV.
In 1486, Inghirami played Phaedra in a performance of Seneca's Phaedra staged by Giovanni Sulpizio da Veroli and Raffaele Riario, with support from the Roman Academy of Julius Pomponius Laetus. After this performance, he was known by the nickname "Phaedra" for the rest of his life.
In 1495, Inghirami was invited to the basilica of Santa Maria sopra Minerva to delivered his "Panegyricus in memoriam divi Thomae Aquinatis" for the annual March 7 celebration of the feast day of St. Thomas Aquinas for the Dominican studium generale, the future Pontifical University of St. Thomas Aquinas (Angelicum) in Rome.
That same year Pope Alexander VI sent Inghirami to be an orator to Maximilian I, Holy Roman Emperor, who made him count palatine and poet laureate. He met Desiderius Erasmus in 1509, becoming a lifelong correspondent and friend. In 1510, he became Librarian of the Vatican Library.
He died on September 6, 1516.