As part of the trade, the Senators also received the Lightning's fourth-round pick in the 2024 NHL Draft.
Joseph has 33 goals and 70 points in 221 games and is a two-time Stanley Cup champion with the Bolts.
In 58 games this year, the Laval, QC., native has eight goals and 18 points.
The 25-year-old is a former teammate of Thomas Chabot, where the two played togther with the QMJHL's Saint John Sea Dogs. The duo won the President's Cup in 2016-17 and also won a silver medal at the 2017 World Juniors.
