A painter and engraver, son of a Florentine goldsmith, Giovanni Battista Vanni, after studying with Aurelio Lomi, entered the workshop of Jacopo da Empoli. In 1618 Vanni enrolled at the Accademia delle Arti del Disegno, and probably by this date the painter had already passed into the workshop of Cristofano Allori.
After the death of Allori, Vanni approached Giulio Parigi, venturing into the creation of sets and theatrical machines.
From 1624 began the first of the numerous Roman stays of Vanni, who, albeit with various interruptions, resided in the papal city several times, also attending that sort of artistic academy that Simon Vouet had gathered in his house, and where he met, among the very numerous, painters such as Orazio and Giovan Battista Riminaldi and Nicolas Poussin.
According to Baldinucci, Vanni traveled to Parma in 1629, a crucial moment in his career, driven to this city by the interest in Correggio's art. From the studio of the Emilian painter Vanni derived the series of beautiful engravings, published in 1642, from the frescoes of the Parma dome of S. Giovanni Evangelista.
Later, while Tuscany remained the center of his activity, Vanni went to Venice, Ferrara and Ravenna. In 1660 the painter was in Pistoia, commissioned by Abbot Ippolito Bracciolini to fresco the minor cloister of the Olivetan monastery of S. Benedetto. While he was intent on these works, Vanni died in Pistoia on 27 July 1660.
As Baldinucci testifies, Vanni was, in the Florentine tradition, an excellent draftsman.