 Hennessy was born on 8 January 1887 at Burwood, Sydney.After completing his secondary education at the Christian Brothers’ High School at Lewisham, and St Patrick's College, Goulburn, he studied architecture at Sydney Technical College and at the University of Pennsylvania.He gained experience with firms in America and Sydney, before becoming a partner with his father John Francis Hennessy trading as Hennessy & Hennessy in 1912.