Financial terms were not released.
The 32-year-old defenseman had 17 points (two goals, 15 assists) in 47 regular-season games with the Tampa Bay Lightning last season but did not play in the Stanley Cup Playoffs because of a lower-body injury.
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"I like his ability to move the puck, his defensive play," Florida general manager Dale Tallon said. "He's steady. He's reliable. He's smart. He'll be a good partner for one of our young guys. I look at a [Mike] Matheson (with Stralman) as a steady influence with him. I think they'll be a good pair."
Selected by the Toronto Maple Leafs in the seventh round (No. 216) of the 2005 NHL Draft, Stralman has 242 points (47 goals, 195 assists) in 795 games with the Lightning, Maple Leafs, New York Rangers and Columbus Blue Jackets. He has 26 points (six goals, 20 assists) in 104 playoff games.