At the age of sixteen Andrea Cellacchi graduated from Conservatorio di Musica Ottorino Respighi in Latina with the highest possible marks. He continued his studies with Francesco Bossone in the master degree programme at the Accademia Nazionale di Santa Cecilia in Rome, and with Matthias Rácz in a specialized master programme at the Hochschule der Kunste Zurich.

In 2016, Andrea Cellacchi was the first Italian to win both the Aeolus International Competition in Düsseldorf and the Muri Competition in Switzerland. Additionally, he won the Premio Abbado in 2015, the Audimozart! Bassoon competition 2016 and the international Fernand Gillet-Hugo Fox bassoon competition in Granada (2018). He won second prize at the Internationaler Instrumentalwettbewerb Markneukirchen.

He was principal bassoon with the Konzerthausorchester in Berlin from 2016-2019. Subsequently, he was principal bassoon with the RAI National Symphony Orchestra in Turin, a position he held until 2021. In April 2022 Andrea Cellacchi joined the Royal Concertgebouw Orchestra as principal bassoon.