The 30-year-old Gaustad joined the Predators in February in a deal that sent a first-round pick this year to Buffalo. The Sabres also received a fourth-round pick in 2013.
Gaustad had seven goals and 10 assists in 56 games last season for Buffalo, and added four assists in 14 games for Nashville. He had a goal and an assist in 10 playoff games.
In seven NHL seasons, he has 71 goals, 114 assists and 591 penalty minutes in 493 games.