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.
For six months, it's a really good accomplishment. But as soon as April [11, the end of the regular season] comes around, no one thinks about the regular season anymore. For six months, it's a real battle to get into the playoffs in the NHL these days. There are a lot of good teams, and it takes consistency over a long time.
— Ducks coach Bruce Boudreau on clinching a playoff berth after a win against the Islanders on Saturday