The contract carries an annual value of $750,000 in the NHL and $150,000 in the AHL.
"We're happy to have Pontus Åberg join our organization," Senators general manager Pierre Dorion said. "He's a scoring winger with a big shot. He's a depth offensive player with good offensive tools and he wants to try North American hockey again this year."
The 27-year-old Swede spent the 2020-21 season in the KHL, where in 49 games with Chelyabinsk Traktor, he had 10 goals and 23 points.
A second round pick by the Predators in 2012, Åberg has played in 132 NHL games with Nashville, Edmonton, Anaheim and Toronto tallying 44 points (17 goals). Additionally, he's suited up in 260 AHL games scoring 97 goals and adding 81 assists.