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. On 30 August 2011 Piccini was loaned to third division club Carrarese, in a season-long deal. He scored his first professional goal on 4 April of the following year, netting the first in a 1–3 home loss against Virtus Lanciano. The following season, Piccini joined Spezia of Serie B on loan until the end of the season. After being an undisputed starter, he was loaned to the top level's Livorno, with a buyout clause.
Betis
On 27 August 2014 Piccini moved to Spanish Segunda División side Real Betis. He made his debut on 7 September, starting in a 1–4 away loss against SD Ponferradina in which he played a part in Jorge Molina's goal, and made 11 more appearances as they won the title. Piccini signed a permanent four-year deal with the Verdiblancos on 9 July 2015, with Fiorentina holding a buyback option. He made his La Liga debut on 23 August, starting in a 1–1 home draw against Villarreal CF. 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, and followed it two months later to open a 1–1 draw at Deportivo de La Coruña. He was also sent off twice over the course of the season, the first coming after 16 minutes of a 3–1 loss at SD Eibar for a foul on Takashi Inui.
On 18 May 2017, Piccini signed a five-year contract with Sporting CP. He made his debut for the club on 6 August, as the Primeira Liga season began with a 2–0 away win against C.D. Aves. Piccini played four games as Sporting won the Taça da Liga. This included the final on 27 January 2018, in which he played all 120 minutes of a 1–1 draw before defeating Vitória F.C. on penalties. On 31 March, he was sent off in a 1–0 loss away to S.C. Braga.
Valencia
On 23 July 2018, Piccini returned to La Liga, signing for Valencia for a fee of around €10 million. 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. 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. 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. He remained sidelined for the whole season, undergoing another operation in May 2020.
International career
Piccini was given his first senior call-up for Italy in October 2018 by manager Roberto Mancini, following injuries to several players in the team. 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.
