Born in Florence, Piccini joined Fiorentina's youth setup in 2002, aged ten, after starting it out at Sporting Arno.

On 5 December 2010, he made his first team – and Serie A – debut, coming on as a substitute for Manuel Pasqual in a 1–0 home win against Cagliari.

[10] On 8 January 2017, Piccini scored his first top-flight goal to conclude a 2–0 win over CD Leganés at the Estadio Benito Villamarín,[11] and followed it two months later to open a 1–1 draw at Deportivo de La Coruña.

[18] In his debut season, he made 37 appearances, mostly as a starter, and scored a last-minute winner in a 2–1 home win over SD Huesca on 23 December.

[19] Seven of these games were in the victorious Copa del Rey run, including 18 minutes as a substitute for Kévin Gameiro in the 2–1 final win over FC Barcelona on 25 May 2019; the result was Valencia's first honour since 2008.

[20] In August 2019, just two games into the new season, Piccini suffered a fractured kneecap while in training, an injury that would leave him out of the squad until the end of year.

[31] He made his senior debut for the national team on 10 October, coming on as an 84th-minute substitute for Alessandro Florenzi in a 1–1 friendly draw against Ukraine in Genoa.