Dossena claimed to be an English-style rugged defender who takes no prisoners and also a powerful attacker. He started his professional career at Verona who were relegated to Seria B in his second season. Dossena joined Treviso in the 2005/6 season, but following the club's relegation from Seria A, Udinese became his co-owners in 2006. Dossena featured at Udinese in 2006-07, joining the club permanently in 2007. His excellent form earned him a call-up to the Italian international team. When John Arne Riise departed for Rome, Rafa Benítez saw Dossena as his replacement. The Italian looked woefully out of sorts in his debut season with Liverpool but confessed to struggling playing further upfield than he was used to in Italy. He did impress in attack when he came on as substitute against Manchester United and Real Madrid and added Liverpool's fourth on each occasion. Dossena was linked with a move to Juventus and Napoli in the summer of 2009 but stayed to fight for his place at Liverpool. However, after making only three starts for the first team in the 2009/10 season, it came as no surprise when he moved to Napoli on a four-year deal in the January transfer window.

Dossena has nailed a regular spot in Napoli's team and played in both Europa League matches against his previous employers in 2010/11, his errant back-pass at Anfield allowing Liverpool to equalise through Steven Gerrard. In 2011/12 Dossena appeared in the Champions League six times as Napoli reached the knock-out stage of the competition, heading a tough group that included Bayern München and Manchester City before being eliminated by the eventual winners, Chelsea.

Dossena moved on loan from Napoli to Palermo in January 2013 and appeared in eleven Serie A matches for the Sicilian club, who were relegated to Serie B at the end of the 2012/13 season. Paolo Di Canio's Sunderland signed Dossena on loan on the last day of the summer transfer window in 2013. Di Canio, however, was soon replaced by the Uruguayan Gustavo Poyet, who played the Italian in only seven Premier League matches plus four domestic cup-ties. The player was released by Sunderland at the end of the season, leaving him a free agent at the age of thirty-two. Dossena signed for League One side Leyton Orient in November 2014 but was released at the end of the season following relegation. He then moved to Switzerland joining second tier side Chiasso, playing nineteen league games for them in 2015/16. Dossena featured in six matches for Piacenza in Seria C in the final months of the 2016/17 season but did not join any other club in the next two campaigns, nor did he announce any retirement from playing.