He began his studies at the Collegio Tolomei in Siena in 1679, before moving to the Seminario Romano in Rome, graduating as a doctor utroque iure on 10 July 1692.
In 1706 the pope intended to make him apostolic nuncio to France, but Banchieri declined the role since it would require him to be ordained a priest.
He was secretary to the Sacra consulta from 3 October 1712 to 1724, then a member of the Special Congregation which discussed the "Riflessioni morali sul Nuovo Testamento" (Moral Reflections on the New Testament) by the Jansenist Pasquier Quesnel..
He took part in the 1730 conclave which elected pope Clement XII, who made Banchieri Secretary of State and prefect of the Sacra Consulta on 15 July 1730, roles he held until his death.
His body lay in state for public veneration before being buried in Santissimo Nome di Gesù church in Pistoia.