The Senators said the first year is a two-way deal worth $750,000 in the NHL and the second is one-way with a value of $825,000.
The 23-year-old Swede was 5-1-2 with a 2.16 goals-against average and a .933 save percentage in nine games for Ottawa last season. He was 5-7-1 in 13 games for Belleville in the American Hockey League.
The Senators selected Gustavsson 55th overall in the 2016 draft.
The Associated Press contributed to this report.