A 1935 graduate of the Royal Military College, Duntroon, where he was the Corps Sergeant Major and was awarded the Sword of Honour, and of the University of Sydney, where he earned a Bachelor of Engineering degree, Brogan served in the Second World War on the staff of New Guinea Force during New Guinea Campaign, and as an observer with the British Army during the Western Allied invasion of Germany.

He presided over the withdrawal of Australian troops from the Vietnam War, the ending of the National Service scheme, and the consequent reduction of the size of the Army, and sweeping organisational changes.

[2][3] Upon receiving his leaving certificate, he was awarded a scholarship to study at the Sydney Technical College;[4] but as part of the Combined Schools team, he played rugby against the Royal Military College, Duntroon, which had moved from Canberra to the Victoria Barracks, Sydney, due to the Great Depression, and decided to go there instead.

[6] In his final year, Brogan was the Corps Sergeant Major, the senior cadet appointment,[7] and on graduation was awarded the Sword of Honour.

[11] When the Second World War broke out in 1939, he sought an appointment with the Second Australian Imperial Force (AIF), but instead was sent to Duntroon as an instructor on 11 November 1939.

[9] He was involved in organising the air supply in support of the Salamaua–Lae campaign,[15] for which he was mentioned in despatches on 23 December 1943,[16] and was appointed an Officer of the Order of the British Empire on 27 April 1944.

[17] He was GSO1 of the Military Training Branch at Allied Land Forces, South West Pacific Area (LHQ) from 5 January 1944 to 6 November 1944.

Soon after he arrived, he came down with malaria, a legacy of his service in New Guinea, to the surprise of the doctors, who were not used to seeing a tropical disease in North West Europe.

Brogan reopened the Land Warfare Centre at Canungra, incorporating lessons from the British Army's experience in the Malayan Emergency.

[20] Brogan served as a brigadier on the staff of the British Army's Far East Land Forces from 1956 to 1958, and went back to Britain once more to attend the Imperial Defence College in 1959.

The Whitlam government swiftly terminated the National Service scheme, causing the manpower of both the Australian Regular Army and the CMF to rapidly shrink.

Brogan revived the position of Vice CGS, appointing Major General Francis Hassett, who would become his successor, to the post.