Florey was born in Adelaide, South Australia, the son of a school principal. He attended St Peter's College, Adelaide, and the University of Adelaide, where he graduated with a Bachelor of Science degree in 1921 and a Doctor of Medicine degree in 1924.
After completing his medical degree, Florey worked at the Walter and Eliza Hall Institute of Medical Research in Melbourne, where he met Ernst Chain. In 1928, they moved to the Sir William Dunn School of Pathology at the University of Oxford, where they began working on the development of penicillin.
Penicillin had been discovered in 1928 by Alexander Fleming, but it had not been developed into a usable drug. Florey and Chain succeeded in isolating the active ingredient of penicillin and purifying it so that it could be injected into patients. They also developed methods for mass-producing penicillin, which made it possible to use it widely during World War II.
Florey and Chain's work on penicillin saved countless lives during World War II and revolutionised the treatment of infectious diseases. Florey was awarded the Nobel Prize in Physiology or Medicine in 1945, and he was knighted in 1944.
Florey was also a distinguished administrator and educator. He served as Vice-Chancellor of the University of Oxford from 1959 to 1962, and he was President of the Royal Society of London from 1960 to 1965. He was also a Fellow of the Australian Academy of Science, the American Academy of Arts and Sciences, and the National Academy of Sciences.
Florey died of a stroke in Oxford in 1968. He is considered one of the most important Australian scientists of the 20th century, and his work on penicillin has saved millions of lives.