Edward Granville Browne was born in 1862, the son of Sir Benjamin Chapman Browne (1839-1917), and his wife, Annie, daughter of Robert Thomas Atkinson. Browne briefly attended Eton College and the Newcastle College of Physical Science (1877-1879), before coming up to Pembroke in 1879 to study Natural Sciences. He was awarded his BA in 1883, having spent the long vacation of 1882 in Constantinople where he continued to develop his knowledge of Persian classical poetry and Sufism, which he had begun to take an interest in whilst studying in Newcastle. After completing his BA, he stayed on at Cambridge and took the Indian Languages tripos in 1884, before resuming his medical studies at St Bartholomew's Hospital, London, qualifying as MD in 1887. He was elected to a Fellowship at Pembroke College in 1887 and from October 1887 to September 1888 he travelled to Persia, for what turned out to be his only trip to the region. During his time away in Persia he was appointed University Lecturer in Persian at the University of Cambridge (1888). In 1902 he was elected Sir Thomas Adams's Professor of Arabic, also at Cambridge. Persia was the focus of his research throughout his life and so it was to be expected that he undertook the cataloguing of the Islamic manuscripts in the Cambridge University Library, as well as 2 smaller collections at the India Office Library (now at the British Library, London). He also oversaw the Foreign Service Students Committee at the University.

He married Alice Caroline, daughter of Francis Henry Blackburne Daniell, a barrister, in June 1906 and they had 2 sons, Patrick and Michael, who later became a High Court judge and a QC respectively. Browne was awarded the Persian Order of the Lion and Sun in 1900, elected as a Fellow of the British Academy in 1903 and as a Fellow of the Royal College of Physicians in 1911. He died on 5 January 1926.