During his long VFL/AFL career, from his debut in 1985, until his retirement in 2001, he gained the reputation as one of the greatest ever full-backs to play the game and was named as full-back in the AFL Team of the Century and is an inductee in the Australian Football Hall of Fame. Prior to 1985 he captained the undefeated Marcellin College 1st XVIII to win both the 1984 Associated Grammar Schools premiership as well as the coveted Herald Shield Cup then  played under lights at the Waverly AFL ground.
He is widely known by his nickname, "SOS" (pronounced "Soss"), standing for "Son of Serge", referring to his father, Sergio Silvagni, another great Carlton player.
Silvagni's defensive skills were renowned and earned him the status as a true clubman at Carlton. In 1996's AFL Team of the Century, Silvagni had the honour of being named at full-back. A title he was bestowed with after it was discovered that players not already in the AFL Hall of Fame were ineligible for selection at the time meaning that players of the quality of David Dench from North Melbourne and Geoff Southby from Carlton two of the games finest Fullbacks were excluded from the selection process even though they later gained entry into the AFL Hall of Fame. He retained the title as the best full-back for four years in succession, although he was also known for his marking and goalkicking ability when playing at the opposite end of the ground in the full-forward position at times, even kicking a bag of 10 goals in Round 16, 1993 against the Fitzroy Lions.
In addition to Silvagni's blanketing tactics, he was also a renowned high-flyer, taking out the Mark of the Year in 1988. However, when one such mark led to an ankle injury, the high-flying aspect of his game largely disappeared.
A year after his retirement at the end of the 2001 season he announced that he would make a comeback to assist Carlton, following their penalties for salary cap infringements. He however changed his mind soon after and was not a listed player for the 2003 season.
Silvangi also played as goalkeeper for the Australian International Rules team on several occasions, and won the inaugural Jim Stynes Medal in 1998.
Silvagni is married to Australian television celebrity, Jo Bailey, and has three sons. Since retiring from playing football he has worked in the media as a guest football commentator and been an assistant coach at four AFL clubs.
Silvagni's second cousin is Fremantle's key defender Alex Silvagni. Alex's father Eric and Stephen's father Sergio are first cousins.