The deal reached Monday will keep the 27-year-old forward away from free agency following the upcoming season. Greening will earn $2 million in the first year of the deal, $2.75 million in the 2015-16 season, and $3.2 million in the final year.
Greening had eight goals and 11 assists with Ottawa in the lockout-shortened 2013 season. He added three goals and an assist in 10 playoff games.
The 6-foot-2, 217-pound Greening has 31 goals and 38 assists in 153 career NHL games.
Greening, a seventh-round draft pick in 2005, won the Calder Cup in 2011 with the Binghamton Senators of the American Hockey League.