The deal with the free agent was announced Thursday.
Shannon played in 79 games with Ottawa last season with 11 goals and 16 assists -- both career highs.
Undrafted out of Boston College, Shannon has 31 goals and 87 points in 260 career NHL games with the Senators, Vancouver, and Anaheim.
Also, Tampa Bay signed minor league left wing Alexandre Picard to a one-year, two-way contract. Picard had 24 goals and 46 points with San Antonio of the AHL last season. He was taken by Columbus in the first round of the 2004 NHL Draft.