Greiss will make $3 million next season, $3.25 million in 2018-19 and $3.75 million in 2019-20, according to a source.
The 31-year-old has a 14-7-3 record with a 2.25 goals-against average and a .928 save percentage this season. His save percentage ranks fifth in the NHL among goaltenders who have played at least 10 games.
He usurped Jaroslav Halak as the Islanders' starter, and the team waived the Slovak goalie and sent him to the American Hockey League.
Last season, after posting a 23-11-4 record during his first regular season with the Islanders, Greiss helped take the club to the second round of the Stanley Cup playoffs for the first time in 23 years.
The Associated Press contributed to this report.