The 33-year-old defenseman had 19 points (two goals, 17 assists) in 75 regular-season games and two points (one goal, one assist) in 14 Stanley Cup Playoff games for the Carolina Hurricanes last season.
Selected by the St. Louis Blues in the first round (No. 18) of the 2007 NHL Draft, Cole has 165 points (29 goals, 136 assists) in 670 regular-season games for the Hurricanes, Minnesota Wild, Colorado Avalanche, Columbus Blue Jackets, Pittsburgh Penguins and Blues and 26 points (two goals, 24 assists) in 110 playoff games.
Cole won the Stanley Cup with the Penguins in 2016 and 2017.
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The Lightning on Wednesday also signed forward Anthony Cirelli ($50 million; $6.25 million AAV) and defensemen Mikhail Sergachev ($60 million; $8.5 million AAV) and Erik Cernak ($41.6 million; $5.2 million AAV) to eight-year contract extensions. Each could have become a restricted free agent after the season.
Forward Vladislav Namestnikov signed a one-year, $2.5 million contract with the Lightning on Wednesday. The 29-year-old had 30 points (16 goals, 14 assists) in 75 regular-season games for the Dallas Stars and Detroit Red Wings last season.
Selected by Tampa Bay in the first round (No. 27) of the 2011 NHL Draft, Namestnikov has 236 points (107 goals, 129 assists) in 553 regular-season games for the Stars, Red Wings, Colorado Avalanche, Ottawa Senators, New York Rangers and Lightning. He has 11 points (six goals, five assists) in 48 playoff games.
Tampa Bay lost to the Colorado Avalanche in six games in the Stanley Cup Final this season. They had won the Cup each of the past two seasons.