Quarterback Alex Tanney, fullback Patrick DiMarco and offensive lineman Bryan Mattison were also let go by the NFL club.
The six-foot-two, 235-pound Greenwood joined the Chiefs as an undrafted free agent after being selected in the first round, third overall, of the 2010 CFL draft by the Toronto Argonauts.
Greenwood, a native of Kingston, Ont., who played collegiately at Concordia, appeared in 48 games with Kansas City, mostly on special teams. Last season, the 27-year-old recorded 10 tackles, one forced fumble and one fumble recovery in 16 games.
During his three seasons with the Chiefs, Greenwood accumulated 34 tackles.
Greenwood played at Concordia from 2006 to '09. In his final season with the Stingers, he captured the Presidents' Trophy as Canadian university football's top defensive player.
Tanney spent time on the Chiefs' practice squad but never made the active roster.
DiMarco started four of the five games he played in last season. But he became expendable when the Chiefs drafted fullback Braden Wilson last weekend and then traded cornerback Javier Arenas to the Arizona Cardinals for another fullback, Anthony Sherman.
Mattison played 19 games over three seasons with Kansas City, St. Louis and Baltimore.Suggest a correction