Cochrane was born in Melbourne in 1950. He completed an honours degree at La Trobe University in 1974 and a doctorate at the University of Adelaide in 1978. After working for a couple of years in the Parliamentary Library of South Australia and as a tutor at the University of Adelaide, he published his first book Industrialisation and Dependence: Australia's Road to Economic Development, 1870–1939 in 1980.[2]
In 2004, Cochrane published a collection of photos from the First World War called The Great War: 1916–1918.[5] He published a book of photographs from the 1941 Siege of Tobruk in 2005.[6]
Cochrane published Colonial Ambition: Foundations of Australian Democracy, which told the story of the introduction of responsible government to New South Wales. It was funded by the New South Wales Government to mark the 150th anniversary of that event.[7]Colonial Ambition shared the inaugural Prime Minister's Prize for History with Les Carlyon's The Great War.[1]
Cochrane's Best We Forget: The War for White Australia, 1914–18 was published in 2018.[8]
In November 2019 Cochrane's The Making of Martin Sparrow was shortlisted for the Voss Literary Prize.[9]