He was given a two-year, one-way contract that TSN reports is worth $2.3 million.
Tampa Bay acquired Lee from Ottawa in exchange for Matt Gilroy on Feb. 26. He played 20 games with the Lightning, recording eight assists and 17 shots on goal while averaging 17:05 in ice time per game.
Over the course of the 2011-12 season, Lee set career-highs for games played (55), assists (15) and points (16). He played the first 35 games with the Senators, who selected him in the first round (No. 9) of the 2005 NHL Draft.
Lee, 25, has played in 187 career games and has five goals and 31 points. He made his NHL debut during the 2007-08 season.
Lee played college hockey at the University of North Dakota and appeared in 82 games over two seasons. He twice represented the United States at the World Junior Championships.