Dossena began his playing career for Torino in 1976, and moved to Pistoiese the following season. He subsequently played for Cesena and Bologna, before returning to Torino in 1981, where he remained until 1987; it was during this second spell with the club that he was a member of the Italian national team, even earning a call-up for the Italy squad at the 1982 FIFA World Cup. He then played for Udinese, Sampdoria and Perugia, where he retired in 1992. Dossena is mostly remembered for his time with Sampdoria, where he achieved notable domestic and international success, winning the 1988–89 Coppa Italia, the 1989–90 European Cup Winners' Cup, the 1990–91 Serie A title, and the 1991 Supercoppa Italiana, also losing out on the 1990 European Super Cup final to European Cup winners and Serie A rivals Milan.