The 35-year-old Czech forward had only 12 points (2-10) in 42 games with the Philadelphia Flyers and Edmonton Oilers. He became an unrestricted free agent July 1.
"Petr will be a huge draw for our fans, and due to many years of experience in the NHL we also expect him to take a large share of responsibility (for the team)," Sparta manager Petr Briza said in a statement.
Nedved has 717 points (310-407) in 982 career NHL games. Nedved had played for Sparta during the NHL's 2004-05 lockout season with 22 goals and 13 assists in 44 games. He also played five games for Sparta during the 1997-98 season when he failed to agree terms on a new contract with the Pittsburgh Penguins.