Butler, 26, split the 2012-13 season between the Predators and New Jersey Devils, combining to total four goals and 11 points in 34 games. Butler previously played three seasons with the Ottawa Senators.
Brennan, 24, split last season between the Panthers and Buffalo Sabres, combining to total three goals and 10 points in 29 games. Brennan was a second-round pick by the Sabres in the 2007 NHL Draft.
Each player can become a restricted free agent this summer.
I'm here to develop a winning culture and a winning team. There is a bright future ahead of this team. A lot of young, great hockey players here and on the way … a fan base that's passionate about the game of hockey.
— Dan Bylsma after being introduced as new coach of the Buffalo Sabres