Streit had been acquired by the Lightning from the Philadelphia Flyers earlier in the day.
Streit will be an unrestricted free agent at the end of this season. Tampa Bay has agreed to retain 50 percent of his salary.
The 39-year-old blueliner had 21 points (5G-16A) in 49 games with the Flyers this year, where he was logging 19:23 overall minutes, with 2:32 of that time on ice coming on the power play.
The 5-foot-11, 191-pound native of Bern, Switzerland has played in 11 NHL seasons for the Canadiens, Islanders and Flyers, producing 428 points (95G-333A) in 765 games. He has 13 points (4G-9A) in 31 career NHL playoff contests.
An offensive-minded, lefthanded-shooting defender, Streit has exceeded the 40-point threshold six times, including just three years ago when he posted 52 points (9G-43A) in 81 games with the Flyers.
The Canadiens originally drafted Streit in the ninth round (262nd overall) in the 2004 NHL Draft.
