Browne was an honorary physician at MRI from 1853-1878. He was the son of George Buckstone Browne, a gentleman and Methodist preacher. Browne was educated at Glasgow University and King's College London, and received his MRCS in 1844, and MD in 1848. Although he was originally a Methodist, he later joined a Congregationalist denomination.
Browne was appointed a lecturer at Manchester Royal School of Medicine in forensic medicine, and later medicine. In 1846 he became a physician at Chorlton-on-Medlock Dispensary, before being elected to an honorary post at MRI in 1853. He was interest in classical literature and biblical study, and published a study of St. John and a triglot dictionary of spiritual words in Hebrew, Greek and English. He was the father of Sir George Buckstone Browne. A bust of Browne is kept at the University of Manchester Medical School.