Born in Sora, Lazio, Zappacosta joined hometown's Sora's youth setup in 1998, aged six. In 2006–07 season, he was a player of Sora's under-15 team in Lazio Region Giovanissimi League. In 2008, he moved to neighbouring Isola Liri, appearing in Campionato Nazionale Dante Berretti under-20's, and made his senior debut for the side in the 2009–10 campaign; obtaining a total of 14 caps and one goal in the league. In January 2011 Zappacosta joined Atalanta in a co-ownership deal for €60,000 transfer fee.
On 31 August 2011, at age 19, he was signed by Avellino where he played for three seasons, initially in temporary deal. The loan was turned into a co-ownership deal for €40,000 fee in 2012.
On 4 June 2014 Zappacosta returned to Atalanta, on 10 July 2015 he was sold to Torino, in the same transfer that brought the midfielder Daniele Baselli to Piedmont, for a total of €10 million transfer fee. He scored his first goal for the club on 28 October during a 3–3 draw at home to Genoa.
On 31 August 2017, he was sold to Chelsea for a reported fee of €28 million plus bonuses. He signed a four-year deal at Stamford Bridge. The transfer was completed minutes before the transfer window shut on deadline day.
He made his international debut for Italy on 12 November 2016, against Liechtenstein in a 2018 World Cup qualifying match, starting the match as a right back.
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