The contract pays Dadonov $3.5 million 2020-21, $5 million in 2021-22 and $6.5 million in 2022-23.
Dadonov had 25 goals and 47 points in 69 regular season games with the Florida Panthers last season. Over 281 games, all with the Panthers, the 31-year-old has scored 91 goals and 202 points.
"We're thrilled to have come to an agreement with Evgenii," said Senators general manager Pierre Dorion in a statement. "He's an elite offensive talent and a very consistent scorer as demonstrated by his point totals over the last three seasons. This is a key signing for us as it adds a player who will help us produce offensively and one with a proven track record on the power-play."