Gaudette was claimed off waivers by Ottawa on Saturday, Elliotte Friedman of Sportsnet reports.
Chicago waived the 25-year-old Friday after making him a healthy scratch on multiple occasions this season. With 58 points in 168 NHL games, he could jump right into a depth role for the Senators, though it's unclear if they plan to play Gaudette in the AHL or NHL at first.