A Roma youth product, Amelia spent most of his professional club career at Livorno, where he made 181 appearances across all competitions, including playing and scoring in the 2006–07 UEFA Cup.

[5] In 2001, he left the Giallorossi to join Serie C1 club Livorno on loan, playing only once in his first season with the Tuscan side; he was successively confirmed by Livorno in the 2002–03 season, for a transfer fee of €2.8 million, as part of the deal that acquired half of Giorgio Chiellini's registration rights for €3.1 million,[6] and promoted as regular by head coach Roberto Donadoni in the club's Serie B comeback campaign.

Amelia then spent two unremarkable loan spells at Lecce and Parma (both Serie A) before returning to Livorno in June 2004, becoming one of the team mainstays since then, and also having his chance to make a debut at European level in the 2006–07 UEFA Cup, where he even managed to score a goal during the group stage, an injury time header in a 1–1 draw against Partizan in November 2006.

[8] Among the highlights of his season, fans mostly remembered Amelia for saving Ronaldinho's penalty in a 3–1 win over Milan, but also, in a more negative fashion, for failing to deal with Giuseppe Mascara's 49-yard strike in the Derby di Sicilia, which ended in a shocking 0–4 home loss for his side.

He spent a few months with amateur side Rocca Priora (where he served as a player and honorary president[17]) before returning to professional football on 9 February 2015, for Serie B club Perugia.

[22] On 8 October 2015, he moved abroad for the first time, signing for English Premier League club Chelsea on a free transfer, on a deal until the end of the season, with the team adding him as back-up goalkeeper to Asmir Begović due to an injury to Thibaut Courtois.

[27][28] Amelia made his senior debut for Italy at age 23, on 16 November 2005, coming on as a second-half substitute in a 1–1 friendly draw against the Ivory Coast, in Geneva.

[27][28][29] He later became a permanent member of Marcello Lippi's squad, and was called up as Italy's third goalkeeper at the 2006 FIFA World Cup, behind Gianluigi Buffon and Angelo Peruzzi, and ahead of reserve Morgan De Sanctis.

[35] On 1 March 2021, he agreed to return at Livorno as the club's new head coach, replacing Alessandro Dal Canto at the helm of the struggling Serie C side.

[36] He failed to save Livorno from relegation to Serie D and left by the end of the season; the club was successively dissolved due to longstanding financial issues.