The team noted that Anderson will earn $5.5 million in 2018-19 and $4 million in 2019-20 for an annual cap hit of $4.75 million.
Among seasons in which he appeared in at least 40 games, the 2016-17 campaign was by far the best of Anderson's career.
The 36-year-old went 25-11-4 during the regular season with a 2.28 goals-against average, .926 save percentage and five shutouts.
Anderson's great play continued during the playoffs to the tune of an 11-8 record, with a 2.34 goals-against average, .922 save percentage and one shutout as part of a run that saw the Sens reach double overtime in Game 7 of the Eastern Conference Final before falling to the Pittsburgh Penguins.
Anderson missed two months of action last season while his wife, Nicholle, had nasopharyngeal carcinoma, a form of cancer.