After the early death of his parents, he grew up with his uncle Francesco Maria Bazzani in Piacenza, who trained him as a musician.
He served in noble families in Barcelona, Florence and Venice, among others, including a post as maestro di capella of Anna Maria Luisa de' Medici.
[1] In 1722 Fürstbischof Johann Philipp Franz von Schönborn engaged him as Hofkapellmeister in Würzburg, together with Giovanni Benedetto Platti.
He returned to Germany with the title and fund of Hofrat (Court Councillor) and directed the private orchestra of Friedrich's brother Wilhelm VIII, von Hessen-Kassel until his death.
During his time in Germany and Sweden Chelleri composed instrumental and church music, including oratorios in Italian.