He can achieve bonuses for games played, time on the ice and various playoff incentives.
The Senators had a magical run last season. After finishing second in the Atlantic Division, they went on a run in the playoffs, eventually losing to the champion Pittsburgh Penguins in seven games in the Eastern Conference finals.
Oduya won Stanley Cups with the Blackhawks in 2013 and 2015, but cap-strapped Chicago couldn't re-sign him after the second title and he went to the Stars.
He helped lead Dallas to the Central Division title in 2015-16, but he suffered a number of injuries last season and the Stars struggled.
The Blackhawks, who had the best record in the West, tried to recapture lightning in a bottle and reacquired Oduya in February. But in a first-round playoff sweep at the hands of the Nashville Predators, the entire Chicago defensive corps looked old and slow.
Oduya also played for the Devils and Thrashers/Jets and won a silver medal with Sweden in the 2014 Olympics.
He had a cap hit of $3.75 million last season.