Paul is in the final season of a two-year, $2.7 million contract ($1.35 million average annual value) he signed with the Senators on Oct. 14, 2020, and could become an unrestricted free agent after the season.
The 27-year-old forward has scored 18 points, including an NHL career-high 11 goals, in 59 games this season. He also led Ottawa in takeaways (48) and was second among forwards in shorthanded ice time per game (2:12).
"We felt we could use more size and physicality from our forward group," Tampa Bay general manager Julien BriseBois said. "We had the opportunity to address that by acquiring Nicholas Paul, who's game is molded for playoff hockey success. He's big and heavy and physical (6-foot-3, 224 pounds), he blocks a lot of shots (41 this season), he can play both center and wing.
"Nick Paul is the type of player we think we can win with. And not just this season, but beyond."
Selected by the Dallas Stars in the fourth round (No. 101) of the 2013 NHL Draft, Paul has scored 66 points (29 goals, 37 assists) in 227 regular-season games with the Senators. He has never played a Stanley Cup Playoff game.
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Joseph is in the final season of a two-year, $1.475 million contract ($737,500 AAV) he signed with the Lightning on Dec. 23, 2020, and could become a restricted free agent after the season.
The 25-year-old forward has scored 18 points (eight goals, 10 assists) in 58 games this season. He was second among Tampa Bay forwards in takeaways (36) and third in shorthanded ice time per game (2:06).
Selected by the Lightning in the fourth round (No. 120) of the 2015 NHL Draft, Joseph has scored 70 points (37 goals, 33 assists) in 221 regular-season games. He also has two assists in 10 playoff games, including winning the Stanley Cup with Tampa Bay in each of the past two seasons.
"Mathieu Joseph was a much appreciated member of our organization and a valued teammate," BriseBois said. "He's worked hard since being drafted to get stronger and turn himself into an NHL player, and he helped our organization win two Stanley Cups."
Tampa Bay (39-16-6) is second in the Atlantic Division, six points behind the Florida Panthers. Ottawa (22-35-5) is seventh in the Atlantic, 31 points behind the Washington Capitals for the second wild card into the playoffs from the Eastern Conference.
This is the second trade the Lightning have made this weekend. They acquired forward Brandon Hagel from the Chicago Blackhawks on Friday for forwards Boris Katchouk and Taylor Raddysh, and a first-round pick in the 2023 NHL Draft and 2024 NHL Draft (top-10 protected). Tampa Bay also received a fourth-round pick in the 2022 NHL Draft and 2024 draft.
"Now we have Brandon new to our group and we have Nick new to our group," BriseBois said. "The coaches are going to have to probably do some experiments with the players that we have and try to find the best combinations."