Tommaso Inghirami was born in Volterra in 1470, the son of Paolo Inghirami, of a noble family of German descent, and of 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.
Inghirami moved to Rome where he was ordained as a deacon of the Papal Chapel in April 1493. 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.
In 1496 Inghirami was sent as part of a delegation from Pope Alexander VI to Maximilian I, Holy Roman Emperor, whom he met in Innsbruck on 14 March 1497. The emperor was so impressed by an oration Inghirami gave that he named him poet laureate and count palatine. On 16 January of the following year, he gave a much-noted eulogy in the presence of the entire papal court at a Memorial Mass for the young John, Prince of Asturias, son of King Ferdinand and Queen Isabel of Spain, held at the Church of San Giacomo degli Spagnuoli.
Inghirami died on either September 5 or 6 in 1516 of injuries he had sustained in 1508 when he fell from his mule and was run over by an oxcart bearing a heavy load of grain.