Of Italian descent and named in the VFL/AFL Italian Team of the Century in 2007, Alessio made his debut in 1992, and was renowned as one of Essendon's great ruckmen. He was reportedly recruited after walking into the clubhouse and asking for a trial, instead of being selected through the player draft. He was given the no. 27 (which had been made famous by Essendon's champion ruckman Simon Madden and has been given to ruckmen ever since). He played in their 2000 premiership team. At the end of 2002, Alessio was delisted and then re-drafted by Essendon, and accepted only match fees during his final season in 2003. At the end of the 2003 season, Alessio called it a day, having played 184 games.
He is now employed by the Essendon FC in a football operations role