"I think we've got a great fit, a player that has the ability to score some goals and a smart player," general manager Jacques Martin said.
He hasn't put up the numbers he is accustomed to over the past couple of seasons due mostly to injury, but Stillman is a steady point producer and power-play specialist who should help a Florida team that hasn't made the playoffs since 2000.
Stillman, 34, scored 24 goals and had 41 assists last season with the Senators and the Hurricanes. He will earn $3.6 million next season and $3.5 million each of the following two seasons.
Stillman had 26 points in 25 postseason games and was plus-14 as Carolina won the Cup in 2006.
"I think he's an individual who will provide leadership through his actions," Martin said. "The fact that he's won two Cups, he could be a mentor to younger players."
Stillman had just one goal and 11 assists in the final 18 games of the most recent regular season, but Martin said he was not too concerned with the drop in production.
"Sometimes when you're acquired at the trade deadline, maybe, I don't know, if it's difficult to fit in," Martin said. "I really believe Cory is a tremendous team player."
Scott Burnside is the NHL writer for ESPN.com. Information from The Associated Press was used in this report.