The deal reportedly is worth $628,000. Greenwood, the starter at strongside linebacker, will be eligible to become an unrestricted free agent following the 2004 season.
Greenwood was one of the Dolphins' four restricted free agents, along with defensive end Adewale Ogunleye, quarterback Sage Rosenfels and running back Travis Minor.
None of them got offer sheets before last Friday's deadline.
In other news:
-- Wide receiver Oronde Gadsden was arrested Monday morning in Pembroke Pines, Fla., on drunk-driving charges and for driving with a suspended license.
Gadsden had attended a charity event Sunday evening related to Jason Taylor's celebrity golf tournament.
In a statement, Gadsden said: "I want to apologize to my family for any harm or embarrassment this may have caused. I also want to apologize to may fans that have supported me over the years and especially to my younger fans that view me as a role model.
"This is a hurdle in my life I will overcome. I take full responsibility for not paying a ticket. It was an oversight on my part and something I should have taken care of. As for the (DUI) charge, it is an accusation that will be cleared by the legal process."
Gadsden is an unrestricted free agent and from the start he wasn't expected to be re-signed by the Dolphins.
-- Brice Hunter, a wide receiver who was a seventh-round pick of the Dolphins in 1996, was shot and killed early Sunday after an argument with a neighbor in Chicago.