Padelli began his playing career at the Seconda Categoria club Delebio, a team from Valtellina. He moved to Lecco in 2001 and then Como the year after. In 2004, he was transferred to Sampdoria, playing for the Primavera youth team, before being loaned to Pizzighettone in the Serie C1 and then Crotone.
On 12 January 2007, Padelli was loaned to Premier League club Liverpool for the duration of the season with the option to make the deal permanent. On the completion of the deal Liverpool manager Rafael Benítez said, "He's a good young goalkeeper who has been selected for his national side. Padelli will give us a good option for the future. The fact he is once again with the under-21s for his national side tells you that we are signing a very good player." He made his debut, and only appearance, for the club on 13 May 2007 against Charlton Athletic F.C. in the last league game of the 2006–07 season to become the first Italian to ever play for the club. However, his poor performance saw him concede two goals in a disappointing draw for the Reds. He returned to Sampdoria on 8 June 2007.
On 5 July 2007 he was officially loaned to Pisa in Serie B, playing several friendly matches for the side as well as making an appearance in the Coppa Italia against Napoli. In the first league game he was left on the bench, playing in the fourth round against Brescia; in the following game, coach Giampiero Ventura selected him over the more experienced Davide Morello. However, his season ended with only 7 appearances with 10 goals conceded. In 2008–09, he was loaned to Avellino with the option to make the deal permanent. With the biancoverdi, he collected 15 appearances with 29 goals conceded, relegating to Lega Pro Prima Divisione at the end of the season. He returned to Sampdoria.
On 2 July 2009 he was transferred from the Genoese club on loan to Bari with a buyout clause, where he served as deputy to Jean-François Gillet. He made his debut in Serie A and with Bari on 9 May 2010 in the match Udinese-Bari. On 29 July 2010 his loan was renewed, with Padelli playing his first game of the 2010–11 season in a 1–1 draw with Palermo.
On 25 June 2011 he returned to Sampdoria, but on 31 August it was announced he had been loaned to Udinese with the option to redeem 50% of his contract in co-ownership. On 27 August 2012, he was sold outright to Udinese, where he spent a season as second-choice goalkeeper, playing 12 times in all competitions.
On 29 May 2013 Padelli was signed by Torino on a free transfer, where, due to the suspension of Gillet, he was a starter. He debuted in the third round of Coppa Italia and conceded twice in a 1–2 loss to Pescara. Padelli played in every match of the 2013–14 season, which concluded with Torino's qualification to the Europa League, collecting 38 appearances. He was awarded the goalkeeping revelation of the season at the Italian Sport Awards on 21 May 2014. He made his official debut in European competition for Torino during the third round of the 2014–15 Europa League against Sweden's Brommapojkarna. After the arrival of Joe Hart from Manchester City, Padelli lost his position in the starting lineup, and finished the season with the expiration of his contract. He concluded his experience at Torino after four seasons and 116 appearances between the league, Coppa Italia and Europa League.
Inter Milan
Padelli was signed by Inter Milan in mid-2017. It was reported that Padelli already agreed to a deal in May in order to formally join the club as a free agent on 1 July. Padelli and his goalkeeping team mate Tommaso Berni signed a new 1-year contract on 28 June 2019. On 2 February 2020, Padelli made his first Serie A appearance for Inter in an away match against Udinese, keeping a clean-sheet in a 2–0 win at Dacia Arena. Padelli became the first choice goalkeeper due to the injury of Samir Handanović.
