It was the first time that the prize, voted for by the members of the Italian Association of Footballers, had been shared in its seven-year history.
Earlier in the ceremony, dubbed the Italian football "Oscars", Czech Nedved beat Roma's Brazilian midfielder Emerson and Romanian striker Adrian Mutu, who moved from Parma to Chelsea last year, to win the award for Best Foreign Player.
Totti came out ahead of international team mates Paolo Maldini of AC Milan and Christian Vieri of Inter Milan in the award for Best Italian Player.
Nedved was also named the European Footballer of the Year and World Soccer Player of the Year last month.
It was a good night for Juventus in the other categories too.
Gianluigi Buffon was voted Best Goalkeeper, while Marcello Lippi pipped AC Milan's Carlo Ancelotti to the award for Best Coach.
The Young Player of the Year trophy went to Roma striker Antonio Cassano, while Pierluigi Collina repeated was voted Best Referee for the second year in a row.
