Forsberg has played in 48 career NHL games with Columbus, Chicago and Carolina going 12-25-4 with a .901 save percentage and a 3.22 goals against average.
"On account of recent injuries, Anton's acquisition provides us with depth and stability at the goaltending position," Senators general manager Pierre Dorion said. "He's a goaltender who's athletic and positionally sound. His addition should prove beneficial for us."
A native of Harnosand, Sweden, the 28-year-old was a seventh round pick (188th overall) in 2011 by the Blue Jackets. He is a two-time AHL All-Star and backstopped the Lake Erie Monsters to the Calder Cup in 2016.
He also won a gold medal at the 2012 World Juniors that were held in Canada.
