Rear-Admiral Greenwood joined the Navy through the ROTP program, attending Royal Roads Military College in Victoria and the Royal Military College of Canada in Kingston graduating in 1979. After two years of training as a Marine Systems Engineer, both in the Fleet and at the Royal Naval Engineering College, he was selected for post-graduate training in naval architecture, attending University College, London University.
Then Lieutenant (N) Greenwood returned to Canada in January 1983 to the Naval Engineering Unit Pacific (NEUP) as the Ship's Architect in the Naval Architecture Division. In July 1985 he was posted as the Canadian Navy Exchange Officer at the David Taylor Naval Ship Research and Development Center (DTNSRDC), outside Washington DC. He was promoted Lieutenant-Commander in January 1986. He subsequently returned to Canada (Ottawa) in July 1988 to the Concept Formulation Section of the Directorate of Maritime Engineering and Maintenance (DMEM) as a project officer for long range procurement projects. After a year as the Acting Section Head for the Naval Architectural Services Section of DMEM, he was promoted to Commander in July 1991 and posted as the Deputy Project Manager (Ship) for the Maritime Coastal Patrol Vessel (MCDV) Project.
In July 1993, Rear-Admiral Greenwood was posted to Halifax as the Naval Architect Officer in the Naval Engineering Unit Atlantic (NEUA). In January 1995, he was posted into Maritime Command Headquarters in an Acting Captain (N) capacity as Deputy Chief of Staff Engineering and Maintenance. Subsequently, in June 1996 he became Commandant of the Canadian Forces Naval Engineering School in Halifax. In May 1999 he became Project Manager of the Submarine Capability Life Extension Project (PM/SCLE) and Director of Maritime Class Management. Submarines (DMCM/Subs). Rear-Admiral Greenwood was promoted to Captain (N) on 1 July 2000 and was appointed Commanding Officer/Fleet Maintenance Facility CAPE BRETON on 3 August 2001. In June 2005, after attending the National Security Studies Course, Rear-Admiral Greenwood was promoted to Commodore and appointed Director General Maritime Equipment Program Management.
In July 2010, he was promoted to his current rank of Rear-Admiral and in August 2010 he took up the position of Commander, Canadian Defence Liaison Staff (Washington) and Canadian Defence Attaché to the United States of America.