Born in Florence, Viviano is a product of Fiorentina and Brescia youth teams. He started his career with a loan in Serie B at Cesena in the 2004–05 season. Then he spent four years as first-choice goalkeeper in Serie B with Brescia.
In January 2009, Viviano was signed by F.C. Internazionale Milano in a co-ownership deal for €3.5 million. He was immediately loaned back to Brescia. In the 2009–10 season he made his debut in Serie A with Bologna where he became the first-choice goalkeeper. Bologna signed him in by purchasing Viviano's 50% registration rights from Brescia also for €3.5 million.
On 25 June 2011, Viviano rejoined Inter Milan from Bologna after Lega Serie A announced the result of co-ownership deals. It was due to an administrative error allowed him to join Inter for a fee of €4.1 million. The error came as the Bologna club director Stefano Pedrelli accidentally halved again the initial €4.71 million valuation of the remaining 50% of his contract to bid only €2.33 million in response to Inter's €4.1 million valuation on the bid submitted to the league office on 24 June. On 23 July 2011, Viviano was diagnosed with a complete tear of the anterior cruciate ligament in the left knee. The injury ruled him out for almost half of the 2011–12 season. in August 2011, Inter swapped Viviano with Juraj Kucka in co-ownership deal, which half of Kucka for €8 million and half of Viviano for €5 million. However both players remained in the original club to wait for the recovery of Viviano. In January 2012, Palermo bought Genoa's half to end their goalkeeper search since summer 2011. He signed a contract which last until 30 June 2016. Viviano would compete with Greek international Alexandros Tzorvas and squeezed Francesco Benussi out. In a separate deal, the transfer fee would partially compensate the signing of Cesare Bovo from Palermo to Genoa outright.
In June 2012, the co-ownership deal of Viviano was renewed between Inter and Palermo; Kucka, however, returned to Genoa from Inter for €6.5 million with youngster Samuele Longo returned to Inter for €7 million; Lesser than a month later, Inter sold Viviano to Palermo outright in another player swap (for Silvestre), making the club eventually received no cash for their €7.6 million investment on Viviano .
In July 2012, Palermo also bought Inter's 50% of the player for €3 million (with Matías Silvestre to Inter on loan also for €3 million), and instantly loaned him to his hometown club Fiorentina for €500,000 with option to buy outright for €7.5 million.
On 2 September 2013, Viviano moved to Premier League team Arsenal on a one-year loan deal with an option to make the move permanent at the end of the season. However, Viviano returned to Palermo at the end of the season without having played a competitive game for Arsenal.
On 12 August 2014, Viviano was signed by Sampdoria in a temporary deal, with an option to sign him outright. On 26 June 2015, the loan was extended with an obligation to purchase. He signed a 1+4 year contract with a transfer fee of €2.3 million (€24,000 loan fee + €2.276 million outright).
He was first choice goalkeeper in the Italy U-20 team at 2005 U-20 World Cup. In 2007 with the Italy U-21 he took part at the U-21 European Championship. He also took part at the 2008 Summer Olympics with the Olympic team. He played once for U-21 team as overage player (de facto U23) on 5 February 2008 against Dutch Olympics team, in order to prepare for the Olympic. The Olympic team was composed of winner from 2007 U-21 Euro, which some of them ineligible to 2009 edition. Viviano did not took part in 2008 Toulon Tournament, however.
Viviano made his debut for Italy senior team on 7 September 2010 during a UEFA Euro 2012 qualifying match, in a 5–0 victory against the Faroe Islands in Florence. At that time he became the second choice goalkeeper for Italy, only after veteran Gianluigi Buffon and ahead of Salvatore Sirigu.